On a Neumann problem with critical exponents and Hardy potentials

In this paper, we consider the Neumann problem of the potential elliptic system with Hardy terms and critical exponents on a bounded domain. Using the critical point theory, we first find infinitely many solutions for the corresponding perturbed subcritical problem. Analyzing concentration points in the bubbles carefully, which appear in the approximate solutions, we establish the concentration estimates, and then obtain infinitely many solutions with positive energy by passing to a limit.