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

Abstract EN

This paper investigates the following p(x)-Laplacian equations with exponential nonlinearities: −Δp(x)u+ρ(x)ef(x,u)=0 in Ω, u(x)→+∞ as d(x,∂Ω)→0, where −Δp(x)u=−div(|∇u|p(x)−2∇u) is called p(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.