# American Institute of Mathematical Sciences

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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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. 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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. 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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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