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

Qihu Zhang

 Department of Mathematics and Information Science, Zhengzhou University of Light Industry, Zhengzhou, Henan 450002, China
Received 18 August 2007; Accepted 25 November 2007

Recommended by M. Garcia-Huidobro

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.