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# Solutions for Semilinear Elliptic Systems with Critical Sobolev Exponent and Hardy Potential

Published:2009-12-04
Printed: Feb 2010
• Mohammed Bouchekif,
Université de Tlemcen, Algérie
• Yasmina Nasri,
Université de Tlemcen, Algérie
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## Abstract

In this paper we consider an elliptic system with an inverse square potential and critical Sobolev exponent in a bounded domain of $\mathbb{R}^N$. By variational methods we study the existence results.
 Keywords: critical Sobolev exponent, Palais--Smale condition, Linking theorem, Hardy potential
 MSC Classifications: 35B25 - Singular perturbations 35B33 - Critical exponents 35J50 - Variational methods for elliptic systems 35J60 - Nonlinear elliptic equations