Positive solutions for singular elliptic equations with critical Hardy-Sobolev exponent

Xiaomei Sun; Wenyi Chen

doi:10.3934/cpaa.2011.10.527

Article Contents

2011, Volume 10, Issue 2: 527-540. Doi: 10.3934/cpaa.2011.10.527

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Positive solutions for singular elliptic equations with critical Hardy-Sobolev exponent

Xiaomei Sun^1, and
Wenyi Chen^1,

1.
School of Mathematics and Statistics, Wuhan University, Wuhan 430072

Received: January 2010

Revised: July 2010

Published: March 2011

Abstract / Introduction Related Papers Cited by

Abstract

In this paper, we consider the following semilinear elliptic equations with critical Hardy-Sobolev exponent:

$ -\Delta u+\lambda\frac{u}{|x-a|^2}-\gamma\frac{u}{|x|^2} =\frac{Q(x)}{|x|^s}|u|^{2^*(s)-2}u+g(x,u), u>0$ in $\Omega,$

$ \frac{\partial u}{\partial\nu}+\alpha(x)u=0 $ on $\partial\Omega. $

By variational method, the existence of positive solution is obtained.

Keywords:

Critical Hardy-Sobolev exponent,
concentration compactness principle.

Mathematics Subject Classification: Primary: 35J20, 35J25; Secondary: 35J65.

Citation:

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