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

Abstract

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