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Mat. Zametki, 2020, Volume 108, Issue 5, Pages 764–770 (Mi mz12737)  

Elliptic Differential-Difference Equations in the Half-Space

A. B. Muravnikab

a "Sozvezdie"
b Peoples' Friendship University of Russia, Moscow

Abstract: The Dirichlet problem in the half-space for elliptic differential-difference equations with operators that are compositions of differential and difference operators is considered. For this problem, classical solvability or solvability almost everywhere (depending on the constraints imposed on the boundary data) is proved, an integral representation of the found solution in terms of a Poisson-type formula is constructed, and its convergence to zero as the time-like independent variable tends to infinity is proved.

Keywords: differential-difference equations, elliptic problems.

Funding Agency Grant Number
Russian Foundation for Basic Research 20-01-00288 А
Ministry of Education and Science of the Russian Federation 5-100
This work was supported by the RUDN Program “5-100” (Secs. 1, 2) and by the Russian Foundation for Basic Research under grant 20-01-00288 A (Secs. 3, 4).


DOI: https://doi.org/10.4213/mzm12737

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English version:
Mathematical Notes, 2020, 108:5, 727–732

UDC: 517.956
Received: 25.03.2020

Citation: A. B. Muravnik, “Elliptic Differential-Difference Equations in the Half-Space”, Mat. Zametki, 108:5 (2020), 764–770; Math. Notes, 108:5 (2020), 727–732

Citation in format AMSBIB
\Bibitem{Mur20}
\by A.~B.~Muravnik
\paper Elliptic Differential-Difference Equations in the Half-Space
\jour Mat. Zametki
\yr 2020
\vol 108
\issue 5
\pages 764--770
\mathnet{http://mi.mathnet.ru/mz12737}
\crossref{https://doi.org/10.4213/mzm12737}
\transl
\jour Math. Notes
\yr 2020
\vol 108
\issue 5
\pages 727--732
\crossref{https://doi.org/10.1134/S0001434620110115}


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