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On a nonlinear nonlocal problem of elliptic type

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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.

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Authors and Affiliations

  1. Central Economics and Mathematics Institute, Russian Academy of Sciences, 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, 2017, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2017, Vol. 57, No. 3, pp. 417–428.

In memory of S.I. Pohozaev

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Solonukha, O.V. On a nonlinear nonlocal problem of elliptic type. Comput. Math. and Math. Phys. 57, 422–433 (2017). https://doi.org/10.1134/S0965542517030149

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  • DOI: https://doi.org/10.1134/S0965542517030149

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