The Behavior Of Several Nonlinear Difference Equations

With the increasing development of natural science and edging field including biology, medicine , theory of control, economies, many mathematical models which are described by difference equations were proposed. Therefore , the study of difference equation plays an important role in theory and practical application. In the past decade, oscillation theory of delay difference has developed very rapidly. With the further study of this direction, the studying contents and methods continuously get abundant. A lots of results have been obtained .This dissertation focuses on the research of the oscillation , asymptotic stability, asymptotication and existence of periodic solutions of several nonlinear difference equations . The paper consists of six chapters. Main contents are as follows:In chapter one, we give a survey to the development and situation of the oscillation of delay difference . We also introduces some preliminary material , including some basic concepts from the oscillation theory of delay difference and some important fixed point theorems.In chapter two, we investigate asymptotic stability , oscillation , asymptotic behavior for the recursive equation, also give the sufficient and necessary condition of existence of the period-2 solution .In chapter three, we are concerned with the even order nonlinear difference equations with nonlinear neutral term. We begin with the study of the relation between first order and higher order. We then make Riccati transformation and establish some...