Oscillation And Nonoscillation For Neutral Difference Equations

In the past twenty years, the theory of difference equations have been proved to be a important tool to establish some mathematic models in many areas. Although a lot of research results have been obtained, there are still some problems that have not been studied.In this paper, we study the oscillation and nonoscillation of second order and higher order neutral difference equations. In the second chapter, we obtain some sufficient conditions of oscillation for second order neutral difference equations, and existence results of nonoscillatory solutions by using the Banach fixed point theorem;In the third chapter, we establish a existence criterion of nonoscilltory solution for higher order neutral difference equations by using Schauder’s fixed point theorem.