Electron. J. Diff. Equ., Vol. 2013 (2013), No. 14, pp. 1-9.

Existence and multiplicity of solutions for Dirichlet problems involving the p(x)-Laplace operator

Mustafa Avci

In this article, we study superlinear Dirichlet problems involving the p(x)-Laplace operator without using the Ambrosetti-Rabinowitz's superquadraticity condition. Using a variant Fountain theorem, but not including Palais-Smale type assumptions, we prove the existence and multiplicity of the solutions.

Submitted November 11, 2011. Published January 14, 2013.
Math Subject Classifications: 35D05, 35J60, 35J70, 58E05.
Key Words: p(x)-Laplace operator; variable exponent Lebesgue-Sobolev spaces; variational approach; Fountain theorem.

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Mustafa Avci
Department of Mathematics, Faculty of Science
Dicle University
21280-Diyarbakir, Turkey
email: mavci@dicle.edu.tr

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