Boundary Value Problems
Volume 2010 (2010), Article ID 584843, 20 pages
doi:10.1155/2010/584843
Research Article

Existence of Solutions for the p(x)-Laplacian Problem with Singular Term

Fu Yongqiang and Yu Mei

Department of Mathematics, Harbin Institute of Technology, Harbin 15000, China

Received 19 August 2009; Accepted 7 March 2010

Academic Editor: Raul F. Manásevich

Copyright © 2010 Fu Yongqiang and Yu Mei. 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 study the following p(x)-Laplacian problem with singular term: -div⁡(|∇u|p(x)-2∇u)+|u|p(x)-2u=λ|u|α(x)-2u+f(x,u), x∈Ω, u=0, x∈∂Ω, where Ω⊂RN is a bounded domain, 1<p-≤p(x)≤p+<N. We obtain the existence of solutions in W01,p(x)(Ω).