Solution Of The Difference Equation With Sign-changing Green's Functions

In this paper,the homoclinic solutions of Second Order Difference Equations and Fourth Order Difference Equations are analyzed,and then the homoclinic solutions of n-order difference equations with sign changing Green functions are considered.We study the existence of homoclinic solutions of n-order nonlinear difference equations with parameter dependence by using second-order difference equations and fourth-order difference equations.So we discusses the Green function of phase equation,and gives the exact expression of the Green function,and obtains the parameter range of the Green function with constant sign or changing sign.In this paper,we establish some existence results for the liner differential equation boundary value problem by using the classical fixed point theorem and the fixed point index theory of Skey.