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On an Elliptic Differential-Difference Equation with Nonsymmetric Shift Operator

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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.

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Correspondence to O. V. Solonukha.

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Original Russian Text © O. V. Solonukha, 2018, published in Matematicheskie Zametki, 2018, Vol. 104, No. 4, pp. 604–620.

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Solonukha, O.V. On an Elliptic Differential-Difference Equation with Nonsymmetric Shift Operator. Math Notes 104, 572–586 (2018). https://doi.org/10.1134/S0001434618090237

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