| The properties of the difference equation and the solution of the differential equation are the important research directions in the field of equations.With the rapid development of science and technology,a lot of nonlinear differential equations and differential square problems have emerged in the field of mathematics,physics and biology.In recent decades,the asymptotic and boundedness of the solutions of nonlinear differential equations and differential equations have been greatly developed,and their theories and methods are becoming more and more mature.In recent years,there are many articles on the low order and high order nonlinear difference equations and differential equations,most equations can not find the exact solution,but you can use the appropriate inequalities and Lyapunov function solution of the equation is estimated,and then prove the existence and uniqueness of the solution,boundedness,the stability of qualitative properties.Therefore,this article is based on these bases and uses its method to study.This article is divided into three chapters.The chapter one is the introduction of difference equations and differential equations in recent years research results,and the methods and ideas of the difference equation and differential equation to study the asymptotic behavior and the boundedness.In the chapter two studies boundedness and asymptotic behavior of solutions of two classes of higher order nonlinear difference equations.?(rN-1(n)...?(r1(n)?x(n)))+ f(n,x(n),n-1∑s=n0g(n,s,x(s)))= 0?(rN-1(n)...?(r1(n)?x(n)))+ f(n,x(n))+ g(n,x(n),n-1∑s=n0h(n,s,x(s)))= 0In this paper,a new discrete Bihari inequality is given,and a sufficient condition for the boundedness of solutions is obtained by using the inequality.In the chapter three,studies boundedness and asymptotic behavior of solutions of two classes of higher order nonlinear differential equations.(rn-1(t)...(r1(t)(xp(t))′)′· · ·)′+ f(t,x(t),x(φ(t))= 0... |
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