Composition Operators on Weighted Bergman Spaces of Polydisk

where N ≥ 3, α ∈ (0, N), p N+α N and Rα 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.