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

Abstract

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.

Keywords

• discrete nonlinear Schrödinger equations
• variational methods
• Superlinear
• homoclinic solutions