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Zh. Vychisl. Mat. Mat. Fiz., 2017, Volume 57, Number 3, Pages 417–428 (Mi zvmmf10534)  

This article is cited in 3 scientific papers (total in 3 papers)

On a nonlinear nonlocal problem of elliptic type

O. V. Solonukha

Central Economics and Mathematics Institute, Russian Academy of Sciences, Moscow, Russia

Abstract: The solvability of a nonlinear nonlocal problem of the elliptic type that is a generalized Bitsadze–Samarskii-type problem is analyzed. Theorems on sufficient solvability conditions are stated. In particular, a nonlocal boundary value problem with $p$-Laplacian is studied. The results are illustrated by examples considered earlier in the linear theory (for $p=2$). The examples show that, in contrast to the linear case under the same “nice” nonlocal boundary conditions, for $p>2$, the problem can have one or several solutions, depending on the right-hand side.

Key words: nonlinear nonlocal problem of elliptic type, sufficient solvability conditions, boundary value problem with $p$-Laplacian.

Funding Agency Grant Number
Russian Science Foundation 14-18-01999


DOI: https://doi.org/10.7868/S0044466917030152

Full text: PDF file (273 kB)
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English version:
Computational Mathematics and Mathematical Physics, 2017, 57:3, 422–433

Bibliographic databases:

UDC: 519.63
Received: 26.07.2016

Citation: O. V. Solonukha, “On a nonlinear nonlocal problem of elliptic type”, Zh. Vychisl. Mat. Mat. Fiz., 57:3 (2017), 417–428; Comput. Math. Math. Phys., 57:3 (2017), 422–433

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. O. V. Solonukha, “On an Elliptic Differential-Difference Equation with Nonsymmetric Shift Operator”, Math. Notes, 104:4 (2018), 572–586  mathnet  crossref  crossref  mathscinet  isi  elib
    2. V. V. Liiko, A. L. Skubachevskii, “Silno ellipticheskie differentsialno-raznostnye uravneniya so smeshannymi kraevymi usloviyami v tsilindricheskoi oblasti”, Trudy Matematicheskogo instituta im. S.M. Nikolskogo RUDN, SMFN, 65, no. 4, Rossiiskii universitet druzhby narodov, M., 2019, 635–654  mathnet  crossref
    3. V. V. Liiko, A. L. Skubachevskii, “Mixed Problems for Strongly Elliptic Differential-Difference Equations in a Cylinder”, Math. Notes, 107:5 (2020), 770–790  mathnet  crossref  crossref  mathscinet  isi  elib
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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