Existence and Asymptotic Behavior of Boundary Blow-Up Solutions for Weightedp(x)-Laplacian Equations with Exponential Nonlinearities

Abstract

This paper investigates the followingp(x)-Laplacian equations with exponential nonlinearities:−Δp(x)u+ρ(x)ef(x,u)=0inΩ,u(x)→+∞asd(x,∂Ω)→0, where−Δp(x)u=−div(|∇u|p(x)−2∇u)is calledp(x)-Laplacian,ρ(x)∈C(Ω). The asymptotic behavior of boundary blow-up solutions is discussed, and the existence of boundary blow-up solutions is given.