Solutions for Semilinear Elliptic Systems with Critical Sobolev Exponent and Hardy Potential 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 potentialCategories:35B25, 35B33, 35J50, 35J60