Multiple homoclinic solutions for discrete Schrödinger equations with perturbed and sublinear terms

Multiple solutions for Schrödinger lattice systems with asymptotically linear terms and perturbed terms

“…To the best of our knowledge, there are only four published papers [3,4,5,6] focusing on PSL systems. The authors [3,4] only obtained the existence of one solution of (1.1) with g n (s) being sub-linear and asymptotically-linear as |s| → ∞, respectively, and the authors [5,6] obtained the existence of two solutions of (1.1) with g n (s) being super-linear and sub-linear as |s| → ∞, respectively. However, in this paper, we obtain the existence of two solutions of (1.1) with g n (s) being asymptotically-linear as |s| → ∞.…”