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

This paper investigates the problem{−Δp(x)u+f(x,u)=0in Ω,u(x)→+∞as d(x,∂Ω)→0, where −Δp(x)u=−div(|∇u|p(x)−2∇u)−Δp(x)u=−div(|∇u|p(x)−2∇u) is called p(x)p(x)-Laplacian. The existence of blow-up solutions is discussed, and the singularity of blow-up solutions is given.