Fixed Point Theory and Applications
Volume 2010 (2010), Article ID 120646, 7 pages
doi:10.1155/2010/120646
Research Article

Existence and Localization Results for p(x)-Laplacian via Topological Methods

B. Cekic and R. A. Mashiyev

Department of Mathematics, Dicle University, 21280 Diyarbakir, Turkey

Received 23 February 2010; Revised 16 April 2010; Accepted 20 June 2010

Academic Editor: J. Mawhin

Copyright © 2010 B. Cekic and R. A. Mashiyev. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We show the existence of a week solution in W01,p(x)(Ω) to a Dirichlet problem for −Δp(x)u=f(x,u) in Ω, and its localization. This approach is based on the nonlinear alternative of Leray-Schauder.