Existence and asymptotic behavior of blow-up solutions to a class of p(x)-Laplacian problems ✩

This paper investigates the problem − p(x)u+ f (x,u) =0 inΩ, u(x)→+∞ as d(x, ∂Ω)→0, where − p(x)u=−div(|∇u|p(x)−2∇u) is called p(x)-Laplacian. The existence of blow-up solutions is discussed, and the singularity of blow-up solutions is given. © 2006 Elsevier Inc. All rights reserved