Solutions for discrete Schrodinger equations with a nonlocal term

In the present paper, we consider the following discrete Schrodinger equations m(Sigma(k is an element of Z) (vertical bar Delta u(k-1)vertical bar(2) V-k vertical bar u(k)vertical bar(2)))(-Delta(2)u(k-1) + V(k)u(k)) - omega u(k) = f(k)(u(k)) k is an element of Z, where m is a continuous function and V = {V-k} is a positive potential, omega is an element of R, Delta u(k-1) = u(k) - u(k-1) and Delta(2) = Delta(Delta) is the one dimensional discrete Laplacian operator. Under some suitable assumptions on f(k), we prove the existence of nontrivial solutions for this nonlocal problems by variation methods. (C) 2020 Elsevier Ltd. All rights reserved.