Journal of Inequalities and Applications
Volume 2008 (2008), Article ID 279306, 8 pages
doi:10.1155/2008/279306
Research Article
Boundary Blow-Up Solutions to p(x)-Laplacian Equations with Exponential Nonlinearities
Department of Mathematics and Information Science, Zhengzhou University of Light Industry, Zhengzhou, Henan 450002, China
Received 18 August 2007; Accepted 25 November 2007
Academic Editor: M. Garcia-Huidobro
Copyright © 2008 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 exponential nonlinearities −△p(x)u+ef(x,u)=0 in Ω, u(x)→+∞ as d(x,∂Ω)→0, where −△p(x)u=−div(|∇u|p(x)−2∇u) is called p(x)- Laplacian. The
singularity of boundary blow-up solutions is discussed, and the existence of boundary blow-up solutions is given.