April  2013, 6(4): 837-860. doi: 10.3934/dcdss.2013.6.837

On mathematical contributions of Petr Petrovich Zabreĭko

1. 

Department of Mathematical Sciences, University of Texas at Dallas

2. 

Richardson, Texas, 75080

3. 

Mathematics Institute, National Academy of Sciences of Belarus

4. 

11 Surganov str., Minsk 220072

5. 

Department of Mathematical Sciences

6. 

University of Texas at Dallas

7. 

Richardson, TX 75080

8. 

Department of Mechanics and Mathematics, Belorussian State University

9. 

4 Nezavisimosti sq., Minsk 220050

Received  February 2012 Published  December 2012

N/A
Citation: Zalman Balanov, I. Gaishun, V. Gorohovik, Wieslaw Krawcewicz, A. Lebedev. On mathematical contributions of Petr Petrovich Zabreĭko. Discrete & Continuous Dynamical Systems - S, 2013, 6 (4) : 837-860. doi: 10.3934/dcdss.2013.6.837
References:
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P. P. Zabreĭko and S. O. Strygina, Cesari's equation and Galerkin's method for finding periodic solutions of ordinary differential equations,, (Ukrainian), 7 (1970), 583. Google Scholar

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P. P. Zabreĭko and Ju. V. Pokornyĭ, A special metric space related to a convex set,, (Russian), 1 (1976), 48. Google Scholar

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P. P. Zabreĭko and S. V. Smickih, A theorem of M. G. Krein and M. A. Rutman,, (Russian), 13 (1979), 81. Google Scholar

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P. P. Zabreĭko and N. M. Isakov, Reduction principle for the method of successive approximations and invariant manifolds,, (Russian), 20 (1979), 539. Google Scholar

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Yu. Appell and P. P. Zabreĭko, Condensing operators in the theory of implicit functions,, (Russian), 165 (1980), 3. Google Scholar

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P. P. Zabreĭko, On the homotopy theory of periodic vector fields,, (Russian), 162 (1980), 3. Google Scholar

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P. P. Zabreĭko, M. A. Krasnosel'skiĭ and A. I. Povolotskiĭ, Spiderwebs of eigenvectors of potential operators,, (Russian), 162 (1981), 62. Google Scholar

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P. P. Zabreĭko and P. P. Zlepko, A generalization of the Newton-Kantorovich method on an equation with nondifferentiable operators,, (Russian) Ukrain. Mat. Z., 34 (1982), 365. Google Scholar

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P. P. Zabreĭko, On the theory of integral operators. II,, (Russian), 169 (1982), 80. Google Scholar

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P. P. Zabreĭko, The domain of convergence of the method of successive approximations for linear equations,, (Russian), 29 (1985), 201. Google Scholar

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J. Appell and P. P. Zabreĭko, Analytic superposition operators,, (Russian), 29 (1985), 878. Google Scholar

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P. P. Zabreĭko and Nguen Khong Tkhai, On the theory of Orlicz spaces of vector-functions,, (Russian), 31 (1987), 116. Google Scholar

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P. P. Zabreĭko and Ya. V. Radyno, Applications of fixed-point theory to the Cauchy problem for equations with degrading operators,, (Russian), 23 (1987), 345. Google Scholar

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P. P. Zabreĭko, Ideal spaces of vector functions,, (Russian), 31 (1987), 298. Google Scholar

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P. P. Zabreĭko and D. F. Nguen, The majorant method in the theory of Newton-Kantorovich approximations and the Pták error estimates,, Numer. Funct. Anal. Optim., 9 (1987), 671. doi: 10.1080/01630568708816254. Google Scholar

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J. Appell and P. P. Zabrejko, On the degeneration of the class of differentiable superposition operators in function spaces,, Analysis, 7 (1987), 305. Google Scholar

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P. P. Zabreĭko and T. A. Makarevich, A Generalization of the Banach - Caccioppoli principle to operators in pseudometric spaces,, (Russian), 23 (1987), 1497. Google Scholar

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P. P. Zabreĭko and T. A. Makarevich, The fixed point theorem and a theorem of L.V. Ovsyannikov,, (Russian), 3 (1987), 53. Google Scholar

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J. Appell, O. W. Diallo and P. P. Zabrejko, On linear integro-differential equations of Barbashin type in spaces of continuous and measurable functions,, J. of Integral Equations Appl., 1 (1988), 227. doi: 10.1216/JIE-1988-1-2-227. Google Scholar

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J. Appell, I. Massabo, A. Vignoli and P. P. Zabrejko, Lipschitz and Darbo conditions for the superposition operator in ideal spaces,, Ann. Mat. Pura Appl., 152 (1988), 123. doi: 10.1007/BF01766144. Google Scholar

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P. P. Zabreĭko and Nguen Khong Tkhaĭ, Linear integral operators in ideal spaces of vector functions,, (Russian), 32 (1988), 587. Google Scholar

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P. P. Zabreĭko and Dyk Fien Nguyen, Pták's estimates in the Newton-Kantorovich method for operator equations,, (Russian), 3 (1989), 8. Google Scholar

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P. P. Zabreĭko and B. A. Godunov, The nature of the convergence of successive approximations for equations with smooth operators,, (Russian), 33 (1989), 583. Google Scholar

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P. P. Zabreĭko, Existence and uniqueness theorems for solutions of the Cauchy problem for differential equations with worsening operators,, (Russian), 33 (1989), 1068. Google Scholar

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J. Appell and P. P. Zabrejko, Continuity properties of the superposition operator,, J. Austral. Math. Soc. Ser. A, 47 (1989), 186. Google Scholar

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J. Appell and P. P.Zabrejko, Boundedness properties of the superposition operator,, Bulletin of the Polish Academy of Sciences. Mathematics, 37 (1989), 363. Google Scholar

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J. Appell, Nguyen Hong Thai and P. P. Zabrejko, General existence theorems for quasilinear elliptic systems without monotonicity,, Journal of Mathematical Analysis and Applications, 145 (1990), 26. doi: 10.1016/0022-247X(90)90428-I. Google Scholar

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U. U. Diallo and P. P. Zabreĭko, Conditions for the asymptotic stability of solutions of Barbashin integro-differential equations,, (Russian), 34 (1990), 101. Google Scholar

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P. P. Zabreĭko, Asymptotic properties of the iterations of linear operators and their applications to approximate methods and to the theory of fixed points,, (Russian), 34 (1990), 485. Google Scholar

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P. P. Zabreĭko and Nguen Khong Tkhai, Cones of vector-functions in Orlicz spaces of vector-functions. Normality and reproducibility properties,, (Russian), 3 (1990), 30. Google Scholar

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P. P. Zabrejko and Nguen Khong Tkhai, Duality theory for ideal spaces of vector-valued functions,, (Russian), 311 (1990), 1296. Google Scholar

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P. P. Zabrejko and Nguen Khong Tkhai, New theorems on the solvability of Hammerstein operator and integral equations,, (Russian), 312 (1990), 28. Google Scholar

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P. P. Zabrejko and S. A. Tersian, On the variational method for solvability of nonlinear integral equations of Hammerstein type,, (Russian), 43 (1990), 9. Google Scholar

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J. Appell and P. P. Zabrejko, Boundedness properties of the superposition operator,, Bulletin of the Polish Academy of Sciences. Mathematics, 37 (1989), 363. Google Scholar

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P. P. Zabrejko, Error estimates for successive approximations and spectral properties of linear operators,, Numerical Functional Analysis and Applications, 11 (1990), 823. doi: 10.1080/01630569008816404. Google Scholar

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P. P. Zabreĭko, The principle of contraction mappings in K-metric and locally convex spaces,, (Russian), 34 (1990), 1065. Google Scholar

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S. A. Tersian and P. P. Zabrejko, Hammerstein integral equations with nontrivial solutions,, Results Math., 19 (1991), 179. Google Scholar

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N. A. Evkhuta and P. P. Zabrejko, The Poincarè method and Samojlenko method for the construction of periodic solutions to ordinary differential equations,, Mathematische Nachrichten, 153 (1991), 85. doi: 10.1002/mana.19911530109. Google Scholar

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J. Appell, E. De Pascale and P. P. Zabrejko, Multivalued superposition operators,, Rend. Sem. Mat. Univ. Padova, 86 (1991), 213. Google Scholar

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P. P. Zabreĭko and Nguen Dyk Fien, Estimates for the rate of convergence of the Newton-Kantorovich method for equations with Hölder linearizations,, (Russian), 2 (1991), 8. Google Scholar

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P. P. Zabrejko and Nguen Khong Tkhai, New results concerning the solvability of Hammerstein operational and integral equations,, (Russian), 27 (1991), 672. Google Scholar

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P. P. Zabrejko and L. G. Tretyakov, Periodic solutions of a quasilinear telegraph equation,, (Russian), 27 (1991), 815. Google Scholar

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J. Appell, E. De Pascale and P. P. Zabrejko, On the application of the Newton-Kantorovic method to nonlinear integral equations of Uryson type,, Numerical Functional Analysis and Optimization, 12 (1991), 271. doi: 10.1080/01630569108816428. Google Scholar

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P. P. Zabreĭko and Nguen Khong Tkhaĭ, Some order properties in Orlicz spaces of vector functions,, (Russian), (1991), 32. Google Scholar

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Nguyen Hong Thai and P. P. Zabrejko, The ideal spaces of vector functions and their applications,, Proceedings of II Conference on Function Spaces (Poznan), (1991), 112. Google Scholar

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P. P. Zabrejko, Abstract relationship principles in the theory of operator equations,, Nonlinear Analysis: Theory, 16 (1991), 817. doi: 10.1016/0362-546X(91)90146-R. Google Scholar

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P. P. Zabreĭko, $C$-theory of linear Fredholm integral equations of the second kind,, (Russian), 3 (1991), 38. Google Scholar

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P. P. Zabreĭko, Implicit function theorems in the theory of nonlinear integral equations,, (Russian), 35 (1995), 975. Google Scholar

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J. Appell, Nguen Hong Thai and P. P. Zabrejko, Multivalued superposition operators in ideal spaces of vector functions. I,, Indag. Math., 2 (1991), 385. doi: 10.1016/0019-3577(91)90025-3. Google Scholar

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J. Appell, Nguen Hong Thai and P. P. Zabrejko, Multivalued superposition operators in ideal spaces of vector functions. II,, Indag. Math., 2 (1991), 397. Google Scholar

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P. P. Zabreĭko, Iterative methods for solving operator equations and their applications to differential equations,, (Russian), (1991), 193. Google Scholar

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J. Appell and P. P. Zabrejko, Linear differential equations in scales of Banach spaces,, Analysis, 12 (1992), 31. Google Scholar

[147]

P. P. Zabrejko and Nguen Van Min', The group of characteristic operators and its applications in the theory of linear ordinary differential equations,, (Russian), 324 (1992), 24. Google Scholar

[148]

P. P. Zabreĭko and Nguen Van Min', Exponential dichotomy and integral manifolds in the theory of flows and their applications,, (Russian), 324 (1992), 515. Google Scholar

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J. Appell, Nguen Hong Thai and P. P. Zabrejko, Multivalued superposition operators in ideal spaces of vector functions. III,, Indag. Math., 3 (1992), 1. doi: 10.1016/0019-3577(92)90023-E. Google Scholar

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P. P. Zabrejko, Iterations methods for the solution of operator equations and their application to ordinary and partial differential equations,, Rendiconti di Matematica. Ser. 7. Roma, 11 (1992), 381. Google Scholar

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J. Appell, A. Carbone and P. P. Zabrejko, Kantorovic majorants for nonlinear operators and applications to Uryson integral equations,, Rendiconti di Matematica. Ser. 7. Roma, 12 (1992), 675. Google Scholar

[152]

J. Appell, O Jong Guk and P. P. Zabrejko, On the Weyl decomposition of the space $D_p^ (O)$ and otrhogonal projections of Navier-Stokes equations,, Annali Univ. Ferrara. Ser. 7: Sci. Mat., 38 (1992), 133. Google Scholar

[153]

P. P. Zabreĭko and Yu. V. Lysenko, A modified Newton-Kantorovich method for finding the minima of smooth functionals,, (Russian), 37 (1993), 106. Google Scholar

[154]

J. Appell, E. De Pascale and P. P. Zabrejko, On the application of the method of successive approximations and the Newton-Kantorovich method to nonlinear functional-integral equations,, Advances in Mathematical Sciences and Applications, 21 (1993), 25. Google Scholar

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B. Aulbach, Nguyen Van Minh and P. P. Zabreiko, A generalization of the monodromy operator for non-periodic linear differential equations,, Differential Equations and Dynamical Systems, 1 (1993), 211. Google Scholar

[156]

N. T. Demidovich, P. P. Zabreĭko and Yu. V. Lysenko, A remark on the Newton-Kantorovich method for nonlinear equations with Hölder linearizations,, (Russian), 4 (1993), 22. Google Scholar

[157]

P. P. Zabreĭko and Yu. V Lysenko, Theorems on the approximation of continuous functions with values in Banach spaces,, (Russian), 4 (1993), 28. Google Scholar

[158]

J. Appell, A. Kufner, O Jong Guk and P. P. Zabrejko, Growth properties of Sobolev space functions over unbounded domains,, Annali Univ. Ferrara. Ser. 7 Sci. Mat., 39 (1993), 55. Google Scholar

[159]

A. B. Antonevich, J. Appell and P. P. Zabrejko, Some remarks on the asymptotic behaviour of iterations of linear operators,, Studia Math., 112 (1994), 1. Google Scholar

[160]

P. P. Zabrejko and T. V. Savchenko, The Banach - Caccioppoli principle and the implicit function theorem in a binormed space and its applications to differential equations,, Diff. Uravn., 30 (1994), 381. Google Scholar

[161]

J. Appell, A. S. Kalitvin and P. P. Zabrejko, Boundary value problems for integro-differential equations of Barbashin type,, Journal of Integral Equations and Applications, 6 (1994), 1. doi: 10.1216/jiea/1181075787. Google Scholar

[162]

J. Appell, E. De Pascale and P. P. Zabrejko, Some remarks on Banach limits,, Atti Sem. Mat. Fis. Univ. Modena, 42 (1994), 273. Google Scholar

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A. K. Abdulazizov, E. De Pascale and P. P. Zabrejko, Il teorema di Bohl sulle soluzioni limitate: Sistemi di infinite equazioni differenziali ordinarie,, Rendiconti Istituto Lombardo, 128 (1994), 37. Google Scholar

[164]

A. Vignoli and P. P. Zabrejko, Some remarks on the Hildebrandt-Graves theorem,, Zeitschrift für Analysis und ihre Anwendungen, 14 (1995), 89. Google Scholar

[165]

E. A. Barkova and P. P. Zabreĭko, Roumieu spaces and the Cauchy problem for linear differential equations with unbounded operators,, (Russian), 39 (1995), 19. Google Scholar

[166]

P. P. Zabreĭko, Implicit functions and operators that are monotone in the sense of Minty in Banach-valued spaces,, (Russian), 39 (1995), 17. Google Scholar

[167]

P. P. Zabreĭko and E. V. Shpilenya, Theorems on the solvability of the Cauchy problem for abstract parabolic equations,, (Russian), 39 (1995), 13. Google Scholar

[168]

B. A. Godunov and P. P. Zabrejko, Geometric characteristics for convergence and asymptotics of successive approximations of equations with smooth operators,, Studia Mathematica, 116 (1995), 225. Google Scholar

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P. P. Zabrejko and V. B. Moroz, New solvability theorems for Hammerstein integral equations with potential nonlinearities,, Differencial'nye Uravnenija, 31 (1995), 690. Google Scholar

[170]

P. P. Zabrejko, $L_2$-theory of Fredholm linear integral equations of the second kind,, Differencial'nye Uravnenija, 31 (1995), 1498. Google Scholar

[171]

J. Appell, E. De Pascale, A. S. Kalitvin and P. P. Zabrejko, On the application of the Newton- Kantorovich method to nonlinear partial integral equations,, Zeitschrift Anal. Anw., 15 (1996), 397. Google Scholar

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V. B. Moroz and P. P. Zabrejko, A variant of the mountain pass theorem and its applications to Hammerstein integral equations,, Zeitschrift für Mathematik, 15 (1996), 985. Google Scholar

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P. P. Zabrejko, The mean theorem for differential mappings in Banach spaces,, Integral Transforms and Special Functions, 4 (1996), 153. doi: 10.1080/10652469608819103. Google Scholar

[174]

J. Appell, E. De Pascale, Ju. V. Lysenko and Zabrejko, New results on Newton-Kantorovich approximations with applications to nonlinear integral equations,, Numerical Functional Analysis and Optimization, 18 (1997), 1. doi: 10.1080/01630569708816744. Google Scholar

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A. Vignoli, P. P. Zabreĭko and V. B. Moroz, Critical values of lower-bounded functionals, and Hammerstein equations,, (Russian), 41 (1997), 16. Google Scholar

[176]

E. A. Barkova and P. P. Zabrejko, Linear differential equations with unbounded operators in Banach spaces,, Zeitschrift für Analysis und ihre Anwendungen, 17 (1998), 339. Google Scholar

[177]

E. De Pascale and P. P. Zabrejko, The convergence of the Newton-Kantorovich method under Vertgeim conditions: A new improvement,, Zeitschrift für Analysis und ihre Anwendungen, 17 (1998), 271. Google Scholar

[178]

V. V. Gorokhovik and P. P. Zabreĭko, Fréchet differentiability of multimappings,, (Russian), 1 (1998), 34. Google Scholar

[179]

P. P. Zabrejko, The fixed point theory and the Cauchy problem for partial differential equations,, (Russian), 1 (1998), 93. Google Scholar

[180]

P. P. Zabreĭko and A. P. Kovalenok, Computation of the index of a singular point of a pseudomonotone vector field. The case of Hilbert spaces,, (Russian), 1 (1998), 107. Google Scholar

[181]

S. V. Zhestkov and P. P. Zabreiko, The Banach-Caccioppoli and Kantorovich principles for the Cauchy problem in the theory of nonlinear systems with partial derivatives,, (Russian), 4 (2000), 48. Google Scholar

[182]

P. P., Zabreĭko and A. P. Kovalenok, On the computation of the asymptotic index of pseudo-monotone vector fields,, (Russian), 44 (2000), 11. Google Scholar

[183]

J. Appell, E. De Pascale and P. P. Zabreĭko, On the unique solvability of Hammerstein integral equations with non-symmetric kernels,, in, 40 (2000), 27. Google Scholar

[184]

F. Cianciaruso, E. De Pascale and P. P. Zabreiko, Some remarks on Newton-Kantorovič approximations,, Atti Sem. Mat. Fis. Univb. Modena, 48 (2000), 207. Google Scholar

[185]

E. De Pascale, P. P. Zabreĭko and N. I. Shirokanova, New conditions for the solvability of Lyapunov-Schmidt integral equations,, (Russian), 44 (2000), 14. Google Scholar

[186]

P. P. Zabrejko, Mark aleksandrovich krasnosel'skii - my teacher and friend,, Izv. Ross. Akad. Estestv. Nauk: Matem., 4 (2000), 5. Google Scholar

[187]

D. Caponetti, E. De Pascale and P. P. Zabreĭko, On the Newton-Kantorovič method in $K$-normed linear spaces,, Rendiconti del Circolo Matematico di Palermo, 49 (2000), 545. doi: 10.1007/BF02904265. Google Scholar

[188]

P. P. Zabreiko and Yu. V. Lysenko, Explicit formulas for higher derivatives of inverse functions in Banach spaces,, (Russian), 4 (2000), 40. Google Scholar

[189]

Z. Balanov, W. Krawcewicz, A. Kushkuley and P. P. Zabreĭko, On a local Lipschitz constant of the maps related to $LU$-decomposition,, Zeitschrift für Analysis und ihre Anwendungen, 19 (2000), 1947. Google Scholar

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E. V. Frolova, A. S. Kalitvin and P. P. Zabrejko, Operator functions with partial integrals on $\mathcal C$ and $L_p$,, Journal of Electrotechnics and Mathematics, 6 (2001), 29. Google Scholar

[191]

P. P. Zabreĭko and Yu. V. Lysenko, Exact formulas for higher-order derivatives of inverse functions in Banach spaces,, (Russian), 45 (2001), 27. Google Scholar

[192]

P. P. Zabreĭko and A. P. Kovalenok, On the existence of nontrivial solutions for a class of elliptic problems,, (Russian), 45 (2001), 34. Google Scholar

[193]

P. P. Zabreĭko and A. P. Kovalenok, On the solvability and existence of nontrivial solutions of the two-dimensional Dirichlet problem,, (Russian), 45 (2001), 5. Google Scholar

[194]

S. V. Zhestkov and P. P. Zabreĭko, On a converse theorem to the fixed point principle in the theory of the Cauchy problem for linear normal partial differential systems,, (Russian), 45 (2001), 12. Google Scholar

[195]

P. P. Zabreiko and Yu. V. Lysenko, Explicit formulas of higher derivatives of implicit functions in Banach spaces,, (Russian), 8 (2001), 114. Google Scholar

[196]

P. P. Zabreiko, On the theory of focusing operators,, (Russian), 3 (2002), 5. Google Scholar

[197]

P. P. Zabreĭko and Yu. V. Lysenko, Explicit formulas for higher-order derivatives of implicit functions,, (Russian), 46 (2002), 8. Google Scholar

[198]

P. P. Zabreĭko, On the Poincaré index of essentially singular points of analytic functions,, (Russian), 46 (2002), 5. Google Scholar

[199]

P. P. Zabreĭko, A. S. Kalitvin and E.V. Frolova, On partial integral equations in the space of continuous functions,, (Russian), 38 (2002), 538. doi: 10.1023/A:1016371902018. Google Scholar

[200]

P. P. Zabreĭko, On global homeomorphism theorem for Gateaux differentiable maps,, (Russian), 1 (2002), 5. Google Scholar

[201]

D. Caponetti and P. P. Zabreĭko, Convex operators in ordered Banach spaces and applications to the Newton-Kantorovič method in $K$-normed linear spaces,, Atti Sem. Mat. Fis. Univ. Modena, 50 (2002), 259. Google Scholar

[202]

E. De Pascale and P. P. Zabreiko, The chord method in Banach spaces and some applications,, Nonlinear Functional Analysis and Applications, 7 (2002), 659. Google Scholar

[203]

E. A. Alekhno and P. P. Zabreĭko, Quasipositive elements and indecomposable operators in ideal spaces. I,, (Russian), 4 (2002), 5. Google Scholar

[204]

E. A. Alekhno and P. P. Zabreĭko, Quasipositive elements and indecomposable operators in ideal spaces. II,, (Russian), 1 (2003), 5. Google Scholar

[205]

P. P. Zabreiko, M.A. Krasnosel'skiĭ and his books. I,, (Russian), (2003), 82. Google Scholar

[206]

S. V. Zhestkov and P. P. Zabrejko, On the nonlocal solvability of the Cauchy problem for quasilinear normal first-order partial differential equations,, Differencial'nye Uravnenya, 39 (2003), 1001. doi: 10.1023/B:DIEQ.0000009203.74756.fd. Google Scholar

[207]

P. P. Zabreĭko and T. V. Tarasik, The Banach-Caccioppoli principle for operators in $K$-normal linear spaces, and stochastic differential equations,, (Russian), 48 (2004), 41. Google Scholar

[208]

E. De Pascale and P.P. Zabreiko, Fixed point theorems for operators in spaces of continuous functions,, Fixed Point Theory, 5 (2004), 117. Google Scholar

[209]

E. A. Barkova and P. P. Zabrejko, An analog of the Peano theorem for fractional-order quasilinear equations in compactly embedding scales of Bansach spaces,, Differencial'nye Uravnenya, 40 (2004), 522. doi: 10.1023/B:DIEQ.0000035793.44173.88. Google Scholar

[210]

P. P. Zabreĭko and O. N. Kirsanova-Evkhuta, A new theorem on the convergence of the minimal residual method,, (Russian), 2 (), 5. Google Scholar

[211]

E. A. Alekhno and P. P. Zabreiko, Weak continuity of superposition operator in ideal spaces with continuous measure,, (Russian), 2 (2004), 21. Google Scholar

[212]

P. P. Zabrejko and N. I. Shirokanova, New existence theorems for Lyapunov-Schmidt integral equations,, Differencial'nye Uravnenya, 40 (2004), 1198. doi: 10.1007/s10625-005-0005-9. Google Scholar

[213]

S. V. Zhestkov and P. P. Zabreĭko, On the construction of invariant Banach spaces and the nonlocal solvability of the Cauchy problem,, (Russian), 3 (2004), 112. Google Scholar

[214]

P. P. Zabreĭko O. N. Kirsanova-Evkhuta, The minimal residual method in Banach spaces,, (Russian), 49 (2005), 5. Google Scholar

[215]

E. A. Alekhno and P. P. Zabreĭko, On the weak continuity of the superposition operator in the space $L_\infty$,, (Russian), 2 (2005), 17. Google Scholar

[216]

P. P. Zabreĭko and A. S. Tykun, The Conley index and the method of guiding functions in the theory of bounded solutions of differential equations,, (Russian), 3 (2005), 13. Google Scholar

[217]

V. V. Gorokhovik and P. P. Zabreiko, On Fréchet differentiability of multifunction,, Optimization, 54 (2005), 391. doi: 10.1080/02331930500100148. Google Scholar

[218]

O. N. Evkhuta and P. P. Zabreĭko, New convergence theorems for Krasnosel'skiĭ-Rutitskiĭ approximations for operator equations in Banach spaces,, (Russian), 49 (2005), 17. Google Scholar

[219]

S. V. Zhestkov and P. P. Zabreĭko, A constructive version of the Meyers theorem for analytic ordinary differential equations,, (Russian), 5 (2005), 11. Google Scholar

[220]

S. V. Zhestkov and P. P. Zabreĭko, The majorant method and the fixed point principle in the nonlocal theory of the Cauchy problem for normal partial differential systems,, (Russian), 42 (2006), 233. doi: 10.1134/S001226610602011X. Google Scholar

[221]

P. P. Zabreĭko and O. Yu. Kushel, The Gantmakher-Kreĭn theorem for binonnegative operators in spaces of functions,, (Russian), 50 (2006), 9. Google Scholar

[222]

P. P. Zabreiko, Some elementary fixed point principle,, in, (2006), 255. Google Scholar

[223]

E. A. Barkova and P. P. Zabreĭko, The Cauchy problem for differential equations of fractional order with deteriorating right-hand sides,, (Russian), 42 (2006), 1132. doi: 10.1134/S0012266106080143. Google Scholar

[224]

S. V. Zhestkov and P. P. Zabreĭko, Nonlocal solvability of the Cauchy problem for a matrix system of ordinary differential equations of Abel-Bernoulli type and the Meyers theorem,, (Russian), 4 (2006), 33. Google Scholar

[225]

S. V. Zhestkov and P. P. Zabreiko, To a problem of nonlocal solvability of the Cauchy problem for Fedorov-Bernouli matrix system with partial derivatives,, (Russian), 14 (2006), 48. Google Scholar

[226]

A. V. Guminskaya and P. P. Zabreĭko, On the calculation of the relative index of a singular point in the nondegenerate case,, (Russian), 1 (2007), 4. Google Scholar

[227]

P. P. Zabreiko, "Applied Equivariant Degree. With a Preface in the Book: Z. Balanov, W. Krawcewicz and H. Steinlein,", (Differential Equations & Dynamical Systems), (2006). Google Scholar

[228]

P. P. Zabreĭko and A. V. Krivko-Krasko, General conditions for a local minimum of smooth functions of two variables,, (Russian), 51 (2007), 11. Google Scholar

[229]

P. P. Zabreĭko and A. V. Krivko-Krasko, Conditions for the local minimum of functions of two variables and the Newton diagram,, (Russian), 51 (2007), 30. Google Scholar

[230]

P. P. Zabreĭko, The open Leontief-Ford model,, Tr. Inst. Mat. (Minsk), 15 (2007), 15. Google Scholar

[231]

P. P. Zabreĭko, On a theorem of M. A. Krasnosel'skiĭ,, (Russian), 52 (2008), 15. Google Scholar

[232]

O. N. Evkhuta and P. P. Zabreiko, A class of iterative methods for solving nonlinear operator equations,, , (2008), 1. Google Scholar

[233]

A. P. Kovalenok and P. P. Zabreiko, The Skrypnik degree theory and boundary value problems,, in, (2008), 181. Google Scholar

[234]

P. P. Zabreĭko and O. Yu. Kushel, Gantmacher - Krein theorem .for bi-nonnegative operators in ideal spaces,, (Russian), 17 (2009), 1. Google Scholar

[235]

P. P. Zabreĭko and O. Yu. Kushel, On a class of linear operators in ideal spaces,, (Russian), (2009), 53. Google Scholar

[236]

P. P. Zabreĭko and Yu. V. Korots, Analysis of implicit successive approximations,, (Russian), 53 (2009), 33. Google Scholar

[237]

P. P. Zabreĭko and A. V. Krivko-Krasko, Systems of scalar equations and implicit functions. I,, Tr. Inst. Mat. (Minsk), 17 (2009), 3. Google Scholar

[238]

E. A. Barkova and P. P. Zabreĭko, Nonlocal theorems on the Cauchy problem for fractional-order differential equations,, (Russian), 54 (2010), 8. Google Scholar

[239]

P. P. Zabreĭko and A. V. Krivko-Krasko, Systems of scalar equations and implicit functions. II,, Tr. Inst. Mat. (Minsk), 18 (2010), 36. Google Scholar

[240]

O. Yu. Kushel and P. P. Zabreiko, Gantmacher - Kreĭn theorem for $2$-totally nonnegative operators in ideal spaces,, Operator Theory: Advances and Applications, 202 (2010), 395. doi: 10.1007/978-3-0346-0158-0_22. Google Scholar

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P. P. Zabreĭko, The continuity and complete continuity of operators of P.S. Uryson,, (Russian), 161 (1965), 1007. Google Scholar

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P. P. Zabreĭko and T. Nurekenov, Existence of non-negative $\omega$-periodic solutions of systems of differential equations,, (Russian), 22 (1966), 32. Google Scholar

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P. P. Zabreĭko and I. B. Ledovskaya, Higher order approximations of the averaging method of N.N. Bogoljubov-N.M. Krylov,, (Russian), 171 (1966), 262. Google Scholar

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P. P. Zabreĭko, R. I. Kacurovskiĭ and M. A. Krasnosel'skiĭ, On a fixed point principle for operators in a Hilbert space,, (Russian), 1 (1967), 93. Google Scholar

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P. P. Zabreĭko and A. I. Povolockiĭ, Theorems on the existence and uniqueness of solutions of Hammerstein equations,, (Russian), 176 (1967), 759. Google Scholar

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P. P. Zabreĭko, M. A. Krasnosel'skiĭ and V. Y. Stecenko, Estimates of the spectral radius of positive linear operators,, (Russian), 1 (1967), 461. Google Scholar

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P. P. Zabreĭko, The spectral radius of Volterra integral operators,, (Russian), 7 (1967), 281. Google Scholar

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P. P. Zabreĭko and M. A. Krasnosel'skiĭ, A way of obtaining new fixed point principles,, (Russian), 176 (1967), 1233. Google Scholar

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P. P. Zabreĭko and M. A. Krasnosel'skiĭ, Simple solutions of operator equations,, (Russian), 2 (1968), 31. Google Scholar

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P. P. Zabreĭko, M. A. Krasnosel'skiĭ and A. V. Pokrovskiĭ, On the problem of bifurcation points,, (Russian), 2 (1968), 41. Google Scholar

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P. P. Zabreĭko and P. Obradovich, On the theory of Banach spaces of vector-valued functions,, (Russian), 10 (1968), 12. Google Scholar

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P. P. Zabreĭko and A. I. Povolotckiĭ, The eigenvectors of Hammerstein's operator,, (Russian), 183 (1968), 758. Google Scholar

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P. P. Zabreĭko and B. P. Kac, On the Nekrasov-Nazarov method of solving nonlinear equations in the case of two-dimensional degeneracy,, (Russian), 3 (1968), 73. Google Scholar

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P. P. Zabreĭko, The Cauchy problem for ordinary differential equations in Banach spaces,, (Russian), 11 (1975), 53. Google Scholar

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P. P. Zabreĭko and Ju. V. Pokornyĭ, A special metric space related to a convex set,, (Russian), 1 (1976), 48. Google Scholar

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P. P. Zabreĭko and S. V. Smickih, A theorem of M. G. Krein and M. A. Rutman,, (Russian), 13 (1979), 81. Google Scholar

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P. P. Zabreĭko and N. M. Isakov, Reduction principle for the method of successive approximations and invariant manifolds,, (Russian), 20 (1979), 539. Google Scholar

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P. P. Zabreĭko and A. V. Zafievskiĭ, Conditions for the extremum of smooth functions,, (Russian), 4 (1979), 76. Google Scholar

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J. Appell and P. P. Zabreĭko, Sharp upper bounds for a superposition operator,, (Russian), 27 (1983), 686. Google Scholar

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J. Appell and P. P. Zabreĭko, Analytic superposition operators,, (Russian), 29 (1985), 878. Google Scholar

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J. Appell and P. P. Zabrejko, On analyticity conditions for the superposition operator in ideal Banach spaces,, Boll. Un. Mat. Ital. C (6), 4 (1985), 279. Google Scholar

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F. Dedagich and P. P. Zabreĭko, On superposition operators in $l_p$ spaces,, (Russian), 28 (1987), 86. Google Scholar

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P. P. Zabreĭko and Nguen Khong Tkhai, On the theory of Orlicz spaces of vector-functions,, (Russian), 31 (1987), 116. Google Scholar

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P. P. Zabreĭko and Ya. V. Radyno, Applications of fixed-point theory to the Cauchy problem for equations with degrading operators,, (Russian), 23 (1987), 345. Google Scholar

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P. P. Zabreĭko, Ideal spaces of vector functions,, (Russian), 31 (1987), 298. Google Scholar

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P. P. Zabreĭko and D. F. Nguen, The majorant method in the theory of Newton-Kantorovich approximations and the Pták error estimates,, Numer. Funct. Anal. Optim., 9 (1987), 671. doi: 10.1080/01630568708816254. Google Scholar

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J. Appell and P. P. Zabrejko, On the degeneration of the class of differentiable superposition operators in function spaces,, Analysis, 7 (1987), 305. Google Scholar

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U. U. Diallo and P. P. Zabreĭko, The Bogolyubov averaging principle in the problem of bounded solutions of Barbashin's integro-differential equations,, (Russian), (1987), 263. Google Scholar

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P. P. Zabreĭko and T. A. Makarevich, A Generalization of the Banach - Caccioppoli principle to operators in pseudometric spaces,, (Russian), 23 (1987), 1497. Google Scholar

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P. P. Zabreĭko and T. A. Makarevich, The fixed point theorem and a theorem of L.V. Ovsyannikov,, (Russian), 3 (1987), 53. Google Scholar

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J. Appell, O. W. Diallo and P. P. Zabrejko, On linear integro-differential equations of Barbashin type in spaces of continuous and measurable functions,, J. of Integral Equations Appl., 1 (1988), 227. doi: 10.1216/JIE-1988-1-2-227. Google Scholar

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J. Appell, I. Massabo, A. Vignoli and P. P. Zabrejko, Lipschitz and Darbo conditions for the superposition operator in ideal spaces,, Ann. Mat. Pura Appl., 152 (1988), 123. doi: 10.1007/BF01766144. Google Scholar

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P. P. Zabreĭko and Nguen Khong Tkhaĭ, Linear integral operators in ideal spaces of vector functions,, (Russian), 32 (1988), 587. Google Scholar

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P. P. Zabreĭko and Dyk Fien Nguyen, Pták's estimates in the Newton-Kantorovich method for operator equations,, (Russian), 3 (1989), 8. Google Scholar

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P. P. Zabreĭko and B. A. Godunov, The nature of the convergence of successive approximations for equations with smooth operators,, (Russian), 33 (1989), 583. Google Scholar

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P. P. Zabreĭko, Existence and uniqueness theorems for solutions of the Cauchy problem for differential equations with worsening operators,, (Russian), 33 (1989), 1068. Google Scholar

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J. Appell and P. P. Zabrejko, Continuity properties of the superposition operator,, J. Austral. Math. Soc. Ser. A, 47 (1989), 186. Google Scholar

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J. Appell and P. P.Zabrejko, Boundedness properties of the superposition operator,, Bulletin of the Polish Academy of Sciences. Mathematics, 37 (1989), 363. Google Scholar

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J. Appell, Nguyen Hong Thai and P. P. Zabrejko, General existence theorems for quasilinear elliptic systems without monotonicity,, Journal of Mathematical Analysis and Applications, 145 (1990), 26. doi: 10.1016/0022-247X(90)90428-I. Google Scholar

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U. U. Diallo and P. P. Zabreĭko, Conditions for the asymptotic stability of solutions of Barbashin integro-differential equations,, (Russian), 34 (1990), 101. Google Scholar

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P. P. Zabreĭko, Asymptotic properties of the iterations of linear operators and their applications to approximate methods and to the theory of fixed points,, (Russian), 34 (1990), 485. Google Scholar

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P. P. Zabrejko and Nguen Khong Tkhai, Duality theory for ideal spaces of vector-valued functions,, (Russian), 311 (1990), 1296. Google Scholar

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P. P. Zabrejko, Error estimates for successive approximations and spectral properties of linear operators,, Numerical Functional Analysis and Applications, 11 (1990), 823. doi: 10.1080/01630569008816404. Google Scholar

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N. A. Evkhuta and P. P. Zabrejko, The Poincarè method and Samojlenko method for the construction of periodic solutions to ordinary differential equations,, Mathematische Nachrichten, 153 (1991), 85. doi: 10.1002/mana.19911530109. Google Scholar

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J. Appell, E. De Pascale and P. P. Zabrejko, Multivalued superposition operators,, Rend. Sem. Mat. Univ. Padova, 86 (1991), 213. Google Scholar

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P. P. Zabreĭko and Nguen Dyk Fien, Estimates for the rate of convergence of the Newton-Kantorovich method for equations with Hölder linearizations,, (Russian), 2 (1991), 8. Google Scholar

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Nguyen Hong Thai and P. P. Zabrejko, The ideal spaces of vector functions and their applications,, Proceedings of II Conference on Function Spaces (Poznan), (1991), 112. Google Scholar

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P. P. Zabreĭko and Nguen Van Min', Exponential dichotomy and integral manifolds in the theory of flows and their applications,, (Russian), 324 (1992), 515. Google Scholar

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J. Appell, O Jong Guk and P. P. Zabrejko, On the Weyl decomposition of the space $D_p^ (O)$ and otrhogonal projections of Navier-Stokes equations,, Annali Univ. Ferrara. Ser. 7: Sci. Mat., 38 (1992), 133. Google Scholar

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P. P. Zabreĭko and Yu. V. Lysenko, A modified Newton-Kantorovich method for finding the minima of smooth functionals,, (Russian), 37 (1993), 106. Google Scholar

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J. Appell, E. De Pascale and P. P. Zabrejko, On the application of the method of successive approximations and the Newton-Kantorovich method to nonlinear functional-integral equations,, Advances in Mathematical Sciences and Applications, 21 (1993), 25. Google Scholar

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N. T. Demidovich, P. P. Zabreĭko and Yu. V. Lysenko, A remark on the Newton-Kantorovich method for nonlinear equations with Hölder linearizations,, (Russian), 4 (1993), 22. Google Scholar

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P. P. Zabreĭko and Yu. V Lysenko, Theorems on the approximation of continuous functions with values in Banach spaces,, (Russian), 4 (1993), 28. Google Scholar

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J. Appell, A. Kufner, O Jong Guk and P. P. Zabrejko, Growth properties of Sobolev space functions over unbounded domains,, Annali Univ. Ferrara. Ser. 7 Sci. Mat., 39 (1993), 55. Google Scholar

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J. Appell, E. De Pascale and P. P. Zabrejko, Some remarks on Banach limits,, Atti Sem. Mat. Fis. Univ. Modena, 42 (1994), 273. Google Scholar

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A. Vignoli and P. P. Zabrejko, Some remarks on the Hildebrandt-Graves theorem,, Zeitschrift für Analysis und ihre Anwendungen, 14 (1995), 89. Google Scholar

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E. A. Barkova and P. P. Zabreĭko, Roumieu spaces and the Cauchy problem for linear differential equations with unbounded operators,, (Russian), 39 (1995), 19. Google Scholar

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P. P. Zabreĭko, Implicit functions and operators that are monotone in the sense of Minty in Banach-valued spaces,, (Russian), 39 (1995), 17. Google Scholar

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P. P. Zabreĭko and E. V. Shpilenya, Theorems on the solvability of the Cauchy problem for abstract parabolic equations,, (Russian), 39 (1995), 13. Google Scholar

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P. P. Zabrejko and V. B. Moroz, New solvability theorems for Hammerstein integral equations with potential nonlinearities,, Differencial'nye Uravnenija, 31 (1995), 690. Google Scholar

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P. P. Zabrejko, The mean theorem for differential mappings in Banach spaces,, Integral Transforms and Special Functions, 4 (1996), 153. doi: 10.1080/10652469608819103. Google Scholar

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E. A. Barkova and P. P. Zabrejko, Linear differential equations with unbounded operators in Banach spaces,, Zeitschrift für Analysis und ihre Anwendungen, 17 (1998), 339. Google Scholar

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V. V. Gorokhovik and P. P. Zabreĭko, Fréchet differentiability of multimappings,, (Russian), 1 (1998), 34. Google Scholar

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P. P. Zabrejko, The fixed point theory and the Cauchy problem for partial differential equations,, (Russian), 1 (1998), 93. Google Scholar

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P. P. Zabreĭko and A. P. Kovalenok, Computation of the index of a singular point of a pseudomonotone vector field. The case of Hilbert spaces,, (Russian), 1 (1998), 107. Google Scholar

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S. V. Zhestkov and P. P. Zabreiko, The Banach-Caccioppoli and Kantorovich principles for the Cauchy problem in the theory of nonlinear systems with partial derivatives,, (Russian), 4 (2000), 48. Google Scholar

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P. P., Zabreĭko and A. P. Kovalenok, On the computation of the asymptotic index of pseudo-monotone vector fields,, (Russian), 44 (2000), 11. Google Scholar

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J. Appell, E. De Pascale and P. P. Zabreĭko, On the unique solvability of Hammerstein integral equations with non-symmetric kernels,, in, 40 (2000), 27. Google Scholar

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P. P. Zabrejko, Mark aleksandrovich krasnosel'skii - my teacher and friend,, Izv. Ross. Akad. Estestv. Nauk: Matem., 4 (2000), 5. Google Scholar

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D. Caponetti, E. De Pascale and P. P. Zabreĭko, On the Newton-Kantorovič method in $K$-normed linear spaces,, Rendiconti del Circolo Matematico di Palermo, 49 (2000), 545. doi: 10.1007/BF02904265. Google Scholar

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P. P. Zabreiko and Yu. V. Lysenko, Explicit formulas for higher derivatives of inverse functions in Banach spaces,, (Russian), 4 (2000), 40. Google Scholar

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Z. Balanov, W. Krawcewicz, A. Kushkuley and P. P. Zabreĭko, On a local Lipschitz constant of the maps related to $LU$-decomposition,, Zeitschrift für Analysis und ihre Anwendungen, 19 (2000), 1947. Google Scholar

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