Electron. J. Diff. Eqns., Vol. 2006(2006), No. 97, pp. 1-10.

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

Maria-Magdalena Boureanu

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.

A corrigendum was posted on December 1, 2006. The author restated Hypothesis (F2) and the proof of Theroem 3.2. See the last page of this manuscript.

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Maria-Magdalena Boureanu
Department of Mathematics
University of Craiova
200585 Craiova, Romania
email: mmboureanu@yahoo.com

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