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

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

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).