Electronic Journal of Differential Equations,
Vol. 2006(2006), No. 97, pp. 1-10.

Title: Existence of solutions for an elliptic equation involving
       the $p(x)$-Laplace operator

Author: Maria-Magdalena Boureanu (Univ. of Craiova, Romania)

Abstract: 
 In this paper we study an elliptic equation involving the
 $p(x)$-Laplace operator on the whole space $\mathbb{R}^N$.
 For that equation we prove the existence of a nontrivial
 weak solution using as main argument the mountain pass
 theorem of Ambrosetti and Rabinowitz.

Submitted June 6, 2006. Published August 22, 2006.
Math Subject Classifications: 35D05, 35J60, 35J70, 58E05, 76A02.
Key Words: $p(x)$-Laplace operator; Sobolev space with variable exponent;
           mountain pass theorem; weak solution.