Existence And Iterative Approximations Of Nonoscillatory Solutions Of Higher Order Functional Differential Equations

Ordinary differential equations have been studied for three hundred years. In the information age, with the rapid development of economic and science, ordinary differ-ential equations still keep growing vigorously, and merges constantly in Physics,Chem-istry,Mechanics,Demography,Biology,Economics etc. In addition, several urgent problems to be solved are raised. For example, stability of motion and control in au-tomatic control, nonlinear vibration in radio-technology, biological prey and multiply, etc.The study of those problems mostly promotes the development of the theory and methods of ordinary differential equations. Therefore, the research on ordinary differ-ential equations is an important subject of theory and practical applications. In the real world, however, the mathematical model on practical problems can come down to delay dynamics system. Strictly speaking, the phenomenon of delay is inevitable, not excepting the system of information transmitted at the speed of light. What's more, compared to ordinary differential equations, functional differential equation is suit-able to describe the real world. Consequently, the research on functional differential equations is full of applications value and challenge in mathematical theory.In this thesis, we study the existence and iterative approximations of nonoscilla-tory solutions of higher order neutral functional differential equations by Brower fixed point theorem.This paper is mainly composed of three chapters.In Chapter 1, we introduce the research background and development situation for neutral delay differential equation. In addition, we introduce the content in this paper.In Chapter 2, we investigate the existence and iterative approximations of nonoscil-latory solutions of the following higher order nonlinear neutral functional differential equations the results generalized the exiting results.In Chapter 3, we investigate the existence and iterative approximations of nonoscil-latory solutions of higher order linear neutral functional differential equationsThe results in this chapter generalize the corresponding results in the exiting paper.