Electron. J. Differential Equations, Vol. 2017 (2017), No. 273, pp. 1-16.

Characterization of solutions to equations involving the p(x)-Laplace operator

Iulia Dorotheea Stircu, Vasile Florin Uta

Abstract:
In this article we study two problems, a nonlinear eigenvalue problem involving the p(x)-Laplacian and a subcritical boundary value problem for the same operator. We work on the variable exponent Sobolev spaces and use one of the variants of the Mountain-Pass Lemma.

Submitted July 27, 2017. Published November 5, 2017.
Math Subject Classifications: 35D30, 35J60, 58E05.
Key Words: Nonlinear eigenvalue problem; p(x)-Laplacian; critical point; variable exponent Sobolev spaces; mountain-pass theorem.

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Iulia Dorotheea Stircu
Department of Mathematics, University of Craiova
200585 Craiova, Romania
email: iulia.stircu@hotmail.com
Vasile Florin Uta
Department of Mathematics, University of Craiova
200585 Craiova, Romania
email: uta.vasi@yahoo.com

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