Existence result for semilinear elliptic systems involving critical exponents

In this paper we deal with the existence of a positive solution for a class of semilinear systems of multi-singular elliptic equations which involve Sobolev critical exponents. In fact, by the analytic techniques and variational methods, we prove that there exists at least one positive solution for the system.

semilinear elliptic system; nontrivial solution; critical exponent; variational method