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On a class of essentially nonlinear elliptic differential-difference equations

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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.

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Authors and Affiliations

  1. Central Economics and Mathematics Institute, Russian Academy of Sciences, Nakhimovskii pr. 47, Moscow, 117418, Russia

    O. V. Solonukha

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  1. O. V. Solonukha
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Correspondence to O. V. Solonukha.

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Original Russian Text © O.V. Solonukha, 2013, published in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2013, Vol. 283, pp. 233–251.

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Solonukha, O.V. On a class of essentially nonlinear elliptic differential-difference equations. Proc. Steklov Inst. Math. 283, 226–244 (2013). https://doi.org/10.1134/S0081543813080154

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