Existence of Solutions for the p(x)‎-Laplacian Problem with the Critical Sobolev-Hardy Exponent

Abstract EN

This paper deals with the p(x)-Laplacian equation involving the critical Sobolev-Hardy exponent.

Firstly, a principle of concentration compactness in W01,p(x)(Ω) space is established, then by applying it we obtain the existence of solutions for the following p(x)-Laplacian problem: -div (|∇u|p(x)-2∇u)+|u|p(x)-2u=(h(x)|u|ps*(x)-2u/|x|s(x))+f(x,u), x∈Ω, u=0, x∈∂Ω, where Ω⊂ℝN is a bounded domain, 0∈Ω, 1