Oscillation Study On The Bounded Solution For Some Kinds Of High Order Nonlinear Difference Equations With Continuous Arguments

The important mathematic implements dealing with the mathematic relations of the discrete fields, with the extensive application of computer science and technology in the fields of science research and production, the theory of difference equations is extensively applied in modern physics, engineering control, economics, even the social science fields and so on. In recent years, the nonlinear difference equations with continuous arguments had been given to great attentions and some evolvements was obtained in its oscillation research works.The paper is devoted to the oscillation research of the bounded solutions of five types of high order nonlinear difference equations with continuous arguments including researches on two classes of high order nonlinear difference delay equations with continuous arguments and three classes of high order nonlinear neutral difference equations. Some sufficient conditions for the oscillation of solutions and bounded solutions have been given for the five different equations. Those topics expand the problems discussed in the previous literatures.The paper is divided into three chapters:In chapter one, the five discussed types of high order nonlinear difference equations have been introduced as well as the brief comments on the history and the methods of the oscillation theory, the preparations of symbols and theory also been made for the oscillation research of the bounded solutions in the following text.In chapter two, two classes of high order nonlinear difference delay equations with continuous arguments have been studied, some sufficient conditions for the oscillation of solutions and bounded solutions has been given for the equations with multi-delay and vary-delay arguments. Those results expand the works in the previous papers.In chapter three, by using analytic technique some sufficient conditions for the oscillation of solutions and bounded solutions for three classes of nonlinear neutral difference equations with continuous arguments, including one order, two order and high order situation. Those results expand the works in the previous papers.