Homoclinic solutions for perturbed discrete Schrödinger systems with concave-convex terms and bounded potentials

By using variational methods, we study a class of discrete nonlinear Schr & ouml;dinger systems, where the potentials are bounded and the nonlinearities are composed of perturbed and concave-convex terms. The main novelties of this paper are as follows: (1) some perturbed terms and concave-convex terms are added to the systems, (2) the weight functions can be sign-changing, and (3) the potentials are bounded, which is essentially different from the unbounded potentials studied before.