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Matematicheskie Zametki, 2021, Volume 110, Issue 1, Pages 90–98
DOI: https://doi.org/10.4213/mzm13009 (Mi mzm13009) 		 
This article is cited in 11 scientific papers (total in 11 papers)

Elliptic Differential-Difference Equations of General Form in the Half-Space

A. B. Muravnik

"Sozvezdie"
Full-text PDF (462 kB) Citations (11)
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DOI: https://doi.org/10.4213/mzm13009
Abstract: We study the Dirichlet problem in the half-space for elliptic differential-difference equations with operators that are compositions of differential operators and shift operators not bound by commensurability conditions for shifts. For this problem, we establish classical solvability or solvability almost everywhere (depending on the constraints imposed on the boundary data), construct an integral representation of the solution by means of a Poisson-type formula, and prove that it approaches to zero as the time-like independent variable tends to infinity.
Keywords: differential-difference equations, elliptic problems, incommensurable shifts.
Funding agency Grant number
Russian Foundation for Basic Research 20-01-00288 A
This work was supported by the Russian Foundation for Basic Research under grant 20-01-00288 A.
Received: 14.01.2021
Revised: 04.03.2021
English version:
Mathematical Notes, 2021, Volume 110, Issue 1, Pages 92–99
DOI: https://doi.org/10.1134/S0001434621070099
Bibliographic databases:
Document Type: Article
UDC: 517.956
Language: Russian
Citation: A. B. Muravnik, “Elliptic Differential-Difference Equations of General Form in the Half-Space”, Mat. Zametki, 110:1 (2021), 90–98; Math. Notes, 110:1 (2021), 92–99
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/mzm13009
  • https://doi.org/10.4213/mzm13009
  • https://www.mathnet.ru/eng/mzm/v110/i1/p90
    • This publication is cited in the following 11 articles:
    1. N. V. Zaitseva, “Classical Solutions of Hyperbolic Differential-Difference Equations”, Diff Equat, 60:7 (2024), 817  crossref
    2. N. V. Zaitseva, “On the Existence of Smooth Solutions to a Hyperbolic Differential-Difference Equation”, Diff Equat, 60:9 (2024), 1153  crossref
    3. Viktoriia V. Liiko, Andrey B. Muravnik, “Elliptic equations with arbitrarily directed translations in half-spaces”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 43 (2023), 64–77  mathnet  crossref
    4. N. V. Zaitseva, A. B. Muravnik, “Klassicheskie resheniya giperbolicheskogo differentsialno-raznostnogo uravneniya so sdvigom na proizvolnyi vektor”, Izv. vuzov. Matem., 2023, no. 5, 34–40  mathnet  crossref
    5. D. I. Borisov, D. M. Polyakov, “Resolvent convergence for differential–difference operators with small variable translations”, Mathematics, 11:20 (2023), 4260  crossref
    6. V. Vasilyev, N. Zaitseva, “Classical solutions of hyperbolic equation with translation operators in free terms”, Mathematics, 11:14 (2023), 3137  crossref
    7. N. V. Zaitseva, A. B. Muravnik, “A Classical Solution to a Hyperbolic Differential-Difference Equation with a Translation by an Arbitrary Vector”, Russ Math., 67:5 (2023), 29  crossref
    8. A. B. Muravnik, “Elliptic Equations with Translations of General Form in a Half-Space”, Math. Notes, 111:4 (2022), 587–594  mathnet  crossref  crossref
    9. N. V. Zaitseva, “Classical Solutions of a Multidimensional Hyperbolic Differential–Difference Equation with Shifts of Various Directions in the Potentials”, Math. Notes, 112:6 (2022), 872–880  mathnet  crossref  crossref
    10. A. B. Muravnik, “Elliptic differential-difference equations with nonlocal potentials in a half-space”, Comput. Math. Math. Phys., 62:6 (2022), 955–961  mathnet  mathnet  crossref  crossref  mathscinet
    11. Zaitseva V N., “Classical Solutions of Hyperbolic Differential-Difference Equations in a Half-Space”, Differ. Equ., 57:12 (2021), 1629–1639  crossref  mathscinet  zmath  isi
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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