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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2024, Volume 64, Number 2, Pages 304–321
DOI: https://doi.org/10.31857/S0044466924020097 (Mi zvmmf11706) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Partial Differential Equations

On the solvability of an essentially nonlinear elliptic differential equation with nonlocal boundary conditions

O. V. Solonukha

Federal Research Center "Computer Science and Control" of Russian Academy of Sciences, 119333, Moscow, Russia
Citations (1)
DOI: https://doi.org/10.31857/S0044466924020097
Abstract: Sufficient conditions for the existence of a generalized solution to a nonlinear elliptic differential equation with nonlocal boundary conditions of Bitsadze–Samarskii type are proved. The strong ellipticity condition is used for an auxiliary differential-difference operator. Under the formulated conditions, the differential-difference operator is demicontinuous, coercive, and has a semibounded variation, so the general theory of pseudomonotone operators can be applied.
Key words: nonlocal problem, differential-difference operator, strong ellipticity condition, operator with semibounded variation.
Received: 13.09.2023
Revised: 13.09.2023
Accepted: 20.10.2023
English version:
Computational Mathematics and Mathematical Physics, 2024, Volume 64, Issue 2, Pages 285–299
DOI: https://doi.org/10.1134/S096554252402012X
Bibliographic databases:
Document Type: Article
UDC: 517.9
Language: Russian
Citation: O. V. Solonukha, “On the solvability of an essentially nonlinear elliptic differential equation with nonlocal boundary conditions”, Zh. Vychisl. Mat. Mat. Fiz., 64:2 (2024), 304–321; Comput. Math. Math. Phys., 64:2 (2024), 285–299
Citation in format AMSBIB
\Bibitem{Sol24}
\by O.~V.~Solonukha
\paper On the solvability of an essentially nonlinear elliptic differential equation with nonlocal boundary conditions
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2024
\vol 64
\issue 2
\pages 304--321
\mathnet{http://mi.mathnet.ru/zvmmf11706}
\crossref{https://doi.org/10.31857/S0044466924020097}
\elib{https://elibrary.ru/item.asp?id=71544524}
\transl
\jour Comput. Math. Math. Phys.
\yr 2024
\vol 64
\issue 2
\pages 285--299
\crossref{https://doi.org/10.1134/S096554252402012X}
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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