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2012 Existence of Solutions for the p ( x ) -Laplacian Problem with the Critical Sobolev-Hardy Exponent
Yu Mei, Fu Yongqiang, Li Wang
Abstr. Appl. Anal. 2012: 1-17 (2012). DOI: 10.1155/2012/894925

Abstract

This paper deals with the p ( x ) -Laplacian equation involving the critical Sobolev-Hardy exponent. Firstly, a principle of concentration compactness in W 0 1 , 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 ) - 2 u = ( h ( x ) | u | p s * ( x ) - 2 u / | x | s ( x ) ) + f ( x , u ) , x Ω , u = 0 , x Ω , where Ω N 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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Yu Mei. Fu Yongqiang. Li Wang. "Existence of Solutions for the p ( x ) -Laplacian Problem with the Critical Sobolev-Hardy Exponent." Abstr. Appl. Anal. 2012 1 - 17, 2012. https://doi.org/10.1155/2012/894925

Information

Published: 2012
First available in Project Euclid: 14 December 2012

zbMATH: 1250.35107
MathSciNet: MR2965446
Digital Object Identifier: 10.1155/2012/894925

Rights: Copyright © 2012 Hindawi

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