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Tr. Mat. Inst. Steklova, 2013, Volume 283, Pages 233–251 (Mi tm3510)  

This article is cited in 5 scientific papers (total in 5 papers)

On a class of essentially nonlinear elliptic differential–difference equations

O. V. Solonukha

Central Economics and Mathematics Institute, RAS, Moscow, Russia

Abstract: An essentially nonlinear differential-difference equation containing the product of the $p$-Laplacian and a difference operator is considered. Sufficient conditions are obtained for the corresponding nonlinear differential-difference operator to be coercive and pseudomonotone in the case of nonvariational statement of the differential equation. The existence of a generalized solution to the Dirichlet problem for the nonlinear equation is proved.

DOI: https://doi.org/10.1134/S0371968513040158

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English version:
Proceedings of the Steklov Institute of Mathematics, 2013, 283, 226–244

Bibliographic databases:

Document Type: Article
UDC: 517.9
Received in September 2012

Citation: O. V. Solonukha, “On a class of essentially nonlinear elliptic differential–difference equations”, Function theory and equations of mathematical physics, Collected papers. In commemoration of the 90th anniversary of Lev Dmitrievich Kudryavtsev's birth, Tr. Mat. Inst. Steklova, 283, MAIK Nauka/Interperiodica, Moscow, 2013, 233–251; Proc. Steklov Inst. Math., 283 (2013), 226–244

Citation in format AMSBIB
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\by O.~V.~Solonukha
\paper On a~class of essentially nonlinear elliptic differential--difference equations
\inbook Function theory and equations of mathematical physics
\bookinfo Collected papers. In commemoration of the 90th anniversary of Lev Dmitrievich Kudryavtsev's birth
\serial Tr. Mat. Inst. Steklova
\yr 2013
\vol 283
\pages 233--251
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm3510}
\crossref{https://doi.org/10.1134/S0371968513040158}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3479958}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2013
\vol 283
\pages 226--244
\crossref{https://doi.org/10.1134/S0081543813080154}
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. L. Skubachevskii, “Boundary-value problems for elliptic functional-differential equations and their applications”, Russian Math. Surveys, 71:5 (2016), 801–906  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    2. Solonukha O.V., “On nonlinear and quasiliniear elliptic functional differential equations”, Discret. Contin. Dyn. Syst.-Ser. S, 9:3 (2016), 869–893  crossref  mathscinet  zmath  isi  elib  scopus
    3. O. V. Solonukha, “On a nonlinear nonlocal problem of elliptic type”, Comput. Math. Math. Phys., 57:3 (2017), 422–433  mathnet  crossref  crossref  isi  elib
    4. O. V. Solonukha, “On an Elliptic Differential-Difference Equation with Nonsymmetric Shift Operator”, Math. Notes, 104:4 (2018), 572–586  mathnet  crossref  crossref  isi  elib
    5. V. A. Popov, “Otsenki reshenii ellipticheskikh differentsialno-raznostnykh uravnenii s vyrozhdeniem”, Differentsialnye i funktsionalno-differentsialnye uravneniya, SMFN, 64, no. 1, Rossiiskii universitet druzhby narodov, M., 2018, 131–147  mathnet  crossref
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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