Journal of Inequalities and Applications 
Volume 2007 (2007), Article ID 19349, 9 pages
doi:10.1155/2007/19349
Research Article

Existence and Asymptotic Behavior of Positive Solutions to p(x)-Laplacian Equations with Singular Nonlinearities

Qihu Zhang

 Department of Mathematics and Information Science, Zhengzhou University of Light Industry, Zhengzhou 450002, Henan, China
Received 17 July 2007; Accepted 27 August 2007

Recommended by M. García-Huidobro

Abstract

This paper investigates the p(x)-Laplacian equations with singular nonlinearities −Δp(x)u=λ/uγ(x) in Ω, u(x)=0 on ∂Ω, where −Δp(x)u=−div(|∇u|p(x)−2∇u) is called p(x)-Laplacian. The existence of positive solutions is given, and the asymptotic behavior of solutions near boundary is discussed.