The Ground State Solutions to Discrete Nonlinear Choquard Equations with Hardy Weights

In this paper, we study the discrete nonlinear Choquard equation is the Green’s function of the discrete fractional Laplacian, which has no singularity but has same asymptotics as the Riesz potential.We assume that V is a bounded periodic potential and 0 lies in a spectral gap of the discrete Schrödinger operator − + V, which makes the functional is strongly indefinite. We prove the existence and asymptotic behavior of ground state solutions by the generalized linking theorem for small ρ ≥ 0.