A system involving fractional Hardy-Schrödinger operators and critical Hardy-Sobolev exponents

We study a system involving fractional Hardy-Schrodinger operators and critical Hardy-Sobolev exponents. Under appropriate conditions, the existence and correlation results of ground state solutions to this system are obtained. To overcome the lack of compactness, we consider a proper approximate problem with subcritical nonlinear terms defined in a bounded domain. Moreover, a compact embedding result for the approximate problem is proved.