On the boundary blow-up solutions of p(x)-Laplacian equations with singular coefficient

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