Multiple solutions for non-periodic Schrödinger lattice systems with perturbation and super-linear terms

Infinitely many homoclinic solutions for sublinear and nonperiodic Schrödinger lattice systems

“…However, there are only few results about the nonperiodic Schrödinger lattice systems [5,9,15,16,22,23]. In particular, in [3,6,7] the authors recently obtained the existence and multiplicity of homoclinic solutions for a class of Schrödinger lattice systems with perturbed 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| → ∞.…”