| At present, many results of the theory of differential equation are researched. With the development of the society, it is widely used not only in economics, ecol-ogy, but also in engineering, finance and other social science. However, many results about the existence for the functional differential equation have been only given suf-ficient conditions for the existence of the solution, but no one has given approximate representation for the solution. In fact, it will be more valuable in the applications if we give an approximate representation for the existence of the functional differential equation.In this thesis, we will study existence and approximation representation for bounded positive solutions of two types of neutral functional differential equations.Firstly, Chapter1introduces the research background and research advance of the functional differential equation. Meanwhile, this chapter also presents contents and methods.Using Banach fixed point theorem, Chapter2shows sufficient conditions of existence of bounded positive solutions for a first order nonlinear neutral functional differential equations In addition, this chapter not only gives the existence of uncountably many bounded positive solutions but also establishes iterative approximate sequence and error es-timate. That is, we give the approximate representations of the bounded positive solutions. So, the results of this chapter are more valuable in the applications.Using Banach fixed point theorem, Chapter3gives sufficient conditions of the existence of bounded positive solutions for second order nonlinear neutral functional differential equation In addition, this chapter not only gives the existence of uncountably many bounded positive solutions but also establishes iterative approximate sequence and error es-timate. That is, we give the approximate representations of the bounded positive solutions. So, the results of this chapter are more valuable in the applications. |
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