Elliptic systems involving critical nonlinearities and different Hardy-type terms

In this paper, a singular system of elliptic equations is investigated, which involves critical nonlinearities and deferent Hardy-type terms. Existence of positive solutions to the system is verified by variational methods and asymptotic properties of solutions at the singular point are established by the Moser iteration method. It is found that the functions in solutions have different singularities at the singular point.