The ground state solutions of nonlinear Schrödinger equations with Hardy weights on lattice graphs

Abstract

In this paper, we study the nonlinear Schrödinger equationon the lattice graph Z N with N ≥ 3, where V is a bounded periodic potential and 0 lies in a spectral gap of the Schrödinger operator −∆+V . Under some assumptions on the nonlinearity f , we prove the existence and asymptotic behavior of ground state solutions with small ρ ≥ 0 by the generalized linking theorem.