Electronic Journal of Differential Equations,
Vol. 2013 (2013), No. 14, pp. 1-9.

Title: Existence and multiplicity of solutions for Dirichlet problems
       involving the p(x)-Laplace operator
        
Author: Mustafa Avci(Dicle Univ.,  Diyarbakir, Turkey)
        
Abstract:
 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.