March  2010, 9(2): 387-395. doi: 10.3934/cpaa.2010.9.387

Begehr-Hile operator and its applications to some differential equations

1. 

Department of Mathematics, Free University Berlin, Arnimallee 3, D-14195 Berlin, Germany

2. 

Department of Mathematics, University of Texas-Pan American, Edinburg, TX 78539

Received  March 2008 Revised  November 2009 Published  December 2009

In the present paper, we are concerned with the integral hierarchy operator defined by Begehr and Hile in 1997. We show that the Begehr--Hile operator $T_{m,n}$ can be interpreted as the iteration of $T$ and $\bar {T}$ under certain conditions. Applications are also illustrated to some differential equations and singular integral equations in the complex plane.
Citation: Hua Liu, Zhaosheng Feng. Begehr-Hile operator and its applications to some differential equations. Communications on Pure & Applied Analysis, 2010, 9 (2) : 387-395. doi: 10.3934/cpaa.2010.9.387
[1]

Guy V. Norton, Robert D. Purrington. The Westervelt equation with a causal propagation operator coupled to the bioheat equation.. Evolution Equations & Control Theory, 2016, 5 (3) : 449-461. doi: 10.3934/eect.2016013

[2]

Mario Ahues, Filomena D. d'Almeida, Alain Largillier, Paulo B. Vasconcelos. Defect correction for spectral computations for a singular integral operator. Communications on Pure & Applied Analysis, 2006, 5 (2) : 241-250. doi: 10.3934/cpaa.2006.5.241

[3]

Noboru Okazawa, Tomomi Yokota. Subdifferential operator approach to strong wellposedness of the complex Ginzburg-Landau equation. Discrete & Continuous Dynamical Systems - A, 2010, 28 (1) : 311-341. doi: 10.3934/dcds.2010.28.311

[4]

Daniel Grieser. A natural differential operator on conic spaces. Conference Publications, 2011, 2011 (Special) : 568-577. doi: 10.3934/proc.2011.2011.568

[5]

András Bátkai, Istvan Z. Kiss, Eszter Sikolya, Péter L. Simon. Differential equation approximations of stochastic network processes: An operator semigroup approach. Networks & Heterogeneous Media, 2012, 7 (1) : 43-58. doi: 10.3934/nhm.2012.7.43

[6]

Radjesvarane Alexandre, Lingbing He. Integral estimates for a linear singular operator linked with Boltzmann operators part II: High singularities $1\le\nu<2$. Kinetic & Related Models, 2008, 1 (4) : 491-513. doi: 10.3934/krm.2008.1.491

[7]

Mohammed Al Horani, Angelo Favini. Inverse problems for singular differential-operator equations with higher order polar singularities. Discrete & Continuous Dynamical Systems - B, 2014, 19 (7) : 2159-2168. doi: 10.3934/dcdsb.2014.19.2159

[8]

Shouchuan Hu, Nikolaos S. Papageorgiou. Nonlinear Neumann equations driven by a nonhomogeneous differential operator. Communications on Pure & Applied Analysis, 2011, 10 (4) : 1055-1078. doi: 10.3934/cpaa.2011.10.1055

[9]

Monika Eisenmann, Etienne Emmrich, Volker Mehrmann. Convergence of the backward Euler scheme for the operator-valued Riccati differential equation with semi-definite data. Evolution Equations & Control Theory, 2019, 8 (2) : 315-342. doi: 10.3934/eect.2019017

[10]

Simona Fornaro, Abdelaziz Rhandi. On the Ornstein Uhlenbeck operator perturbed by singular potentials in $L^p$--spaces. Discrete & Continuous Dynamical Systems - A, 2013, 33 (11&12) : 5049-5058. doi: 10.3934/dcds.2013.33.5049

[11]

Benoît Pausader, Walter A. Strauss. Analyticity of the nonlinear scattering operator. Discrete & Continuous Dynamical Systems - A, 2009, 25 (2) : 617-626. doi: 10.3934/dcds.2009.25.617

[12]

Vittorio Martino. On the characteristic curvature operator. Communications on Pure & Applied Analysis, 2012, 11 (5) : 1911-1922. doi: 10.3934/cpaa.2012.11.1911

[13]

Michel Pierre, Morgan Pierre. Global existence via a multivalued operator for an Allen-Cahn-Gurtin equation. Discrete & Continuous Dynamical Systems - A, 2013, 33 (11&12) : 5347-5377. doi: 10.3934/dcds.2013.33.5347

[14]

Manh Hong Duong, Yulong Lu. An operator splitting scheme for the fractional kinetic Fokker-Planck equation. Discrete & Continuous Dynamical Systems - A, 2019, 39 (10) : 5707-5727. doi: 10.3934/dcds.2019250

[15]

Lianwang Deng. Local integral manifolds for nonautonomous and ill-posed equations with sectorially dichotomous operator. Communications on Pure & Applied Analysis, 2020, 19 (1) : 145-174. doi: 10.3934/cpaa.2020009

[16]

Peter C. Gibson. On the measurement operator for scattering in layered media. Inverse Problems & Imaging, 2017, 11 (1) : 87-97. doi: 10.3934/ipi.2017005

[17]

Bernd Kawohl, Jiří Horák. On the geometry of the p-Laplacian operator. Discrete & Continuous Dynamical Systems - S, 2017, 10 (4) : 799-813. doi: 10.3934/dcdss.2017040

[18]

Yunmei Chen, Xianqi Li, Yuyuan Ouyang, Eduardo Pasiliao. Accelerated bregman operator splitting with backtracking. Inverse Problems & Imaging, 2017, 11 (6) : 1047-1070. doi: 10.3934/ipi.2017048

[19]

Dieter Mayer, Tobias Mühlenbruch, Fredrik Strömberg. The transfer operator for the Hecke triangle groups. Discrete & Continuous Dynamical Systems - A, 2012, 32 (7) : 2453-2484. doi: 10.3934/dcds.2012.32.2453

[20]

Tanja Eisner, Rainer Nagel. Arithmetic progressions -- an operator theoretic view. Discrete & Continuous Dynamical Systems - S, 2013, 6 (3) : 657-667. doi: 10.3934/dcdss.2013.6.657

2018 Impact Factor: 0.925

Metrics

  • PDF downloads (7)
  • HTML views (0)
  • Cited by (1)

Other articles
by authors

[Back to Top]