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 Schrödinger 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.