Ground state solution for a class of discrete superlinear Schrödinger equations

In this paper, we investigate a class of discrete nonlinear Schrödinger equations featuring superlinear nonlinearities. A discrete version of the Palais-Smale sequence decomposition is established for a broad class of nonlinear terms. By innovatively combining the Nehari manifold approach with bounded Palais-Smale sequence decomposition techniques and refined energy estimates, we rigorously prove the existence of nontrivial ground state solutions. Furthermore, we demonstrate that these solutions exhibit rapid exponential decay with precise asymptotic behaviour, which obtained by the comparison principle. Our work extends previous results in the continuous case to the discrete setting while revealing new qualitative properties of localized solutions.