Study On The Oscillation And Asymptotic Behavior For Some Kinds Of Neutral Difference Equations

In recent years, with the development of modern science and technology, people have put forward a great many new neutral difference equations in natural science and social science as biology, economics, demology, physics and control theory, etc. Because of universality of application and a mass of mathematics problems are raised related to itself, we starve for solving them with related mathematical theories. Moreover, oscillation and nonoscillation theory being the key content of qualitative study of the neutral difference equations, it gets prevalent attention people and it is a new investigative realm with blooming life-force. Because of the progress in modern science and technology, the studies about this new academic branch are not only a demand of the development of mathematics theroyies themselves, but also a demand of actual applications.This paper is devoted to the problems of qualitative behavior of the nonlinear neutral difference equations, the neutral difference equations with continuous arguments and the high order neutral difference equations. Some results which have expanded and improved the related conclusion in the previous papers are obtained.Firstly, the thesis studies the oscillation of the nonlinear neutral difference equations , several sufficient conditions for oscillation are obtained.Then, as to the neutral difference equations with continuous arguments. we firstly study the oscillation of the first order nuetral difference equations with continuous arguments, two sufficient conditions for oscillation of solutions are obtained. At the same time, we also study the oscillation of the second order nuetral difference equations with continuous arguments, some sufficient conditions for oscillation of solutions are gived. At last, the oscillation and asymptotic behavior of solutions of the high order difference equations with continuous arguments are discussed, using reduction to absurdity and mathemtics induction, these results expand and improve the conclusions given in the previous papers.In the last paper of this thesis, we study the oscillation of a class of high order nonlinear difference equations. A sufficient condition is obtained. Some existing results in the literatures are improved.