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

Yu Mei, Fu Yongqiang and Li Wang

Abstract and Applied Analysis, 2012, vol. 2012, issue 1

Abstract: 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

Date: 2012
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https://doi.org/10.1155/2012/894925

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:894925

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