Existence of Solution for Singular Elliptic Systems Involving Critical Sobolev-Hardy Exponents

The aim of the contemporary variational theory is to transform the problem of searching the solution of equation or equation system into the problem of investigating the critical point of the corresponding energy function in a suitable space. This paper concerns the existence of solution for a singular quasilinear elliptic system involving two critical Sobolev Hardy exponents. Using Sobolev Hardy inequality, Ekeland’s variation principle and the critical point theorem, the existence of solution was proved under the certain conditions that the coefficients and nonlinear term of the equations meet.