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Matematicheskie Zametki, 2020, Volume 108, Issue 5, Pages 764–770
DOI: https://doi.org/10.4213/mzm12737 (Mi mzm12737) 		 
This article is cited in 12 scientific papers (total in 12 papers)

Elliptic Differential-Difference Equations in the Half-Space

A. B. Muravnikab

a "Sozvezdie"
b Peoples' Friendship University of Russia, Moscow
Full-text PDF (458 kB) Citations (12)
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DOI: https://doi.org/10.4213/mzm12737
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).
Received: 25.03.2020
English version:
Mathematical Notes, 2020, Volume 108, Issue 5, Pages 727–732
DOI: https://doi.org/10.1134/S0001434620110115
Bibliographic databases:
Document Type: Article
UDC: 517.956
Language: Russian
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
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    • This publication is cited in the following 12 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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