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
Department of Mathematics and Information Science, Zhengzhou University of Light Industry, Zhengzhou 450002, Henan, China
Received 17 July 2007; Accepted 27 August 2007
Academic Editor: M. García-Huidobro
Copyright © 2007 Qihu Zhang. 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
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.