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Boundary Value Problem for the φ-Laplacian with Operator Right-Hand Side

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Abstract

Abstract—General sufficient conditions for the existence of a solution of a boundary value problem for the φ-Laplacian with functional boundary conditions are obtained. As a consequence of this result, natural restrictions on the lower and upper functions are obtained under which there exists a solution of a periodic boundary value problem for the φ-Laplacian. Several applications of this results to the proof of the existence of solutions of boundary value problems for higher-order equations are given.

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Authors and Affiliations

  1. University of Latvia, Institute of Mathematics and Computer Science, Riga, LV, 1459, Latvia

    A. Ya. Lepin

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  1. A. Ya. Lepin
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Correspondence to A. Ya. Lepin.

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Original Russian Text © A.Ya. Lepin, 2018, published in Differentsial’nye Uravneniya, 2018, Vol. 54, No. 12, pp. 1604–1609.

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Lepin, A.Y. Boundary Value Problem for the φ-Laplacian with Operator Right-Hand Side. Diff Equat 54, 1560–1565 (2018). https://doi.org/10.1134/S0012266118120030

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  • DOI: https://doi.org/10.1134/S0012266118120030

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