Discrete Schrödinger equations in the nonperiodic and superlinear cases: homoclinic solutions

Abstract

Using variational methods, we study the existence and multiplicity of homoclinic solutions for a class of discrete Schrödinger equations in infinite m-dimensional lattices with nonlinearities being superlinear at infinity. Our results generalize some existing results in the literature by using some weaker conditions.

Perturbed Schrödinger lattice systems: existence of homoclinic solutions

“…Clearly, (1.2) is a special case of (1.1) with f n ≡ 0, a n ≡ −1 and b n = 2 + ε n . The study of (1.1) with f n ≡ 0 has been an active theme of research in the past decade, which can be divided into two cases: the periodic case (see [1-3, 5, 12-15, 17, 18, 20, 24, 25] and so on) and the non-periodic case (see [4,8,9,16,[21][22][23] and so on).…”