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Mat. Zametki, 2018, Volume 104, Issue 4, Pages 604–620 (Mi mz11715)  

On an Elliptic Differential-Difference Equation with Nonsymmetric Shift Operator

O. V. Solonukha

Central Economics and Mathematics Institute Russian Academy of Sciences, Moscow

Abstract: An essentially nonlinear equation containing the product of the $p$-Laplacian and a nonsymmetric difference operator is considered. Sufficient conditions guaranteeing the coercivity and pseudomonotonicity of the corresponding nonlinear difference-differential operator are obtained. The existence of a generalized solution of the Dirichlet problem for the nonlinear equation under consideration is proved.

Keywords: essentially nonlinear elliptic functional-differential equation, pseudomonotone operator, accretive operator.

Funding Agency Grant Number
Russian Foundation for Basic Research 16-01-00450
This work was supported by the Russian Foundation for Basic Research under grant 16-01-00450.


DOI: https://doi.org/10.4213/mzm11715

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English version:
Mathematical Notes, 2018, 104:4, 572–586

Bibliographic databases:

UDC: 517.9
Received: 05.06.2017

Citation: O. V. Solonukha, “On an Elliptic Differential-Difference Equation with Nonsymmetric Shift Operator”, Mat. Zametki, 104:4 (2018), 604–620; Math. Notes, 104:4 (2018), 572–586

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