Existence And Approximate Representation Of Nonoscillatory Solutions For Neutral Delay Differential Equation

There is a long history on theory of differential equation and many results are researched so far. With the development of modern society, it is widely used in en-gineering, ecology, economics, finance etc. However, with the research work of the existence for the functional differential equation, a lot of work has been only given sufficient conditions for existence of the solution, but nobody has given approximate representation for the solution. In fact, it will not be more valuable in the applications until we give approximate representation for the existence of the delay differential equation. In this thesis, we shall study existence and approximation representation for nonoscillatory solutions of two types of neutral delay differential equations.Firstly, Chapter1introduces the research background and current situation of delay differential equation. Then, this chapter also presents contents and methodsUsing Banach fixed point theorem, Chapter2shows sufficient conditions of exis-tence of nonoscillatory solutions for high order delay differential equations In addition, this chapter not only establishs the existence of uncountably many nonoscil-latory solutions but also gives iterative approximate sequence and error estimate. That is, we give the approximate representations of the corresponding nonoscillatory solu-tions. Thus, the results in this chapter are more valuable in the applications.Using the fixed point theorem, Chapter3shows sufficient conditions of existence of nonoscillatory solutions for first order differential equations with several delays In addition, this chapter not only establishs the existence of uncountably many nonoscil-latory solutions but also gives iterative approximate sequence and error estimate. That is, we give the approximate representations of the corresponding nonoscillatory solu-tions. Thus, the results in this chapter are more valuable in the applications.