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 CMFD, 2016, Volume 60, Pages 102–113 (Mi cmfd297)

On the Dirichlet problem for differential-difference elliptic equations in a half-plane

A. B. Muravnikab

a RUDN University, 6 Miklukho-Maklaya st., Moscow, 117198 Russia
b JSC Concern "Sozvezdie", Voronezh, Russia

Abstract: The Dirichlet problem is considered in a half-plane (with continuous and bounded boundaryvalue function) for the model elliptic differential-difference equation
$$u_{xx}+au_{xx}(x+h,y)+u_{yy}=0,\qquad|a|<1.$$
Its solvability is proved in the sense of generalized functions, the integral representation of the solution is constructed, and it is proved that everywhere but the boundary hyperplane this solution satisfies the equation in the classic sense as well.

 Funding Agency Grant Number Ministry of Education and Science of the Russian Federation ÍØ-4479.2014.1 Russian Foundation for Basic Research 14-01-00265

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Citation: A. B. Muravnik, “On the Dirichlet problem for differential-difference elliptic equations in a half-plane”, Proceedings of the Seventh International Conference on Differential and Functional-Differential Equations (Moscow, August 22–29, 2014). Part 3, CMFD, 60, PFUR, M., 2016, 102–113

Citation in format AMSBIB
\Bibitem{Mur16} \by A.~B.~Muravnik \paper On the Dirichlet problem for differential-difference elliptic equations in a~half-plane \inbook Proceedings of the Seventh International Conference on Differential and Functional-Differential Equations (Moscow, August 22--29, 2014). Part~3 \serial CMFD \yr 2016 \vol 60 \pages 102--113 \publ PFUR \publaddr M. \mathnet{http://mi.mathnet.ru/cmfd297} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. Muravnik A.B., “Half-Plane Differential-Difference Elliptic Problems With General-Kind Nonlocal Potentials”, Complex Var. Elliptic Equ.
2. A. B. Muravnik, “Asymptotic Properties of Solutions of the Dirichlet Problem in the Half-Plane for Differential-Difference Elliptic Equations”, Math. Notes, 100:4 (2016), 579–588
3. A. B. Muravnik, “Asimptoticheskie svoistva reshenii dvumernykh differentsialno-raznostnykh ellipticheskikh zadach”, Differentsialnye i funktsionalno-differentsialnye uravneniya, SMFN, 63, no. 4, Rossiiskii universitet druzhby narodov, M., 2017, 678–688
4. A. Muravnik, “On the half-plane Dirichlet problem for differential-difference elliptic equations with several nonlocal terms”, Math. Model. Nat. Phenom., 12:6, SI (2017), 130–143
5. A. B. Muravnik, “Elliptic Problems with Nonlocal Potential Arising in Models of Nonlinear Optics”, Math. Notes, 105:5 (2019), 734–746
6. A. B. Muravnik, “Elliptic Differential-Difference Equations in the Half-Space”, Math. Notes, 108:5 (2020), 727–732
7. V N. Zaitseva, “Global classical solutions of some two-dimensional hyperbolic differential-difference equations”, Differ. Equ., 56:6 (2020), 734–739
8. V N. Zaitseva, “On global classical solutions of hyperbolic differential-difference equations”, Dokl. Math., 101:2 (2020), 115–116
9. A. B. Muravnik, “Elliptic Differential-Difference Equations of General Form in the Half-Space”, Math. Notes, 110:1 (2021), 92–99
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