The spectrum theory of the discrete Schrödinger operator and its application

Abstract

This paper introduces the spectrum theory of discrete Schrödinger operators with different kinds of potentials, including bounded, unbounded, periodic, or complex potentials. The paper also provides exponential estimates of the Green's function and eigenfunctions of the discrete Schrödinger operators. As an application, I review some of our results on standing wave solutions of discrete Schrödinger equations.