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
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