Ground states for a system of nonlinear Schrödinger equations with singular potentials

<p style='text-indent:20px;'>In this paper, we consider the existence and asymptotic behavior of ground state solutions for a class Hamiltonian elliptic system with Hardy potential. The resulting problem engages three major difficulties: one is that associated functional strongly indefinite, second difficulty must overcome lies in verifying link geometry showing boundedness Cerami sequences when nonlinearity different from usual global super-quadratic condition. third singular potential, which does not belong to Kato's class. These enable us develop direct approach new tricks difficulties caused by singularity potential dropping classical assumption on nonlinearity. Our based non-Nehari method developed recently, establish some results Nehari-Pankov type under mild conditions, analyze asymptotical solutions.</p>