Solutions to coupled critical elliptic systems involving attractive Hardy–type terms

Abstract

In this paper, a system of elliptic equations is studied, which involves coupled critical nonlinearities and attractive Hardy terms. By the local compactness analysis of (PS)c sequence and estimates on extremal functions corresponding to the best Sobolev constant, the existence of Mountain–Pass solutions is proved. Secondly, the asymptotic properties at the origin of solutions to the system are proved by the analytic technics and variational arguments.