Existence of Solutions for the p(x)-Laplacian Problem with the Critical Sobolev-Hardy Exponent
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∇...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/894925 |
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| Summary: | 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<p-≤p(x)≤p+<N, and f(x,u) satisfies p(x)-growth conditions. |
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| ISSN: | 1085-3375 1687-0409 |