Quasilinearization Method For A Class Of Functional Differential Systems With Retardation And Anticipation

With the increasing development of natural science, in the field of natural science including physics, theory of control, biology, medicine, economies and edging field, many mathematical models which are described by differential equations are proposed. Differential equations are powerful tools that describe the law of nature, but it is difficult to find their general solutions. Therefore, there has been an increasing interest in the study of the nature of solutions of differ-ential equation in theory.This paper will use monotone iterative technique to research functional differential systems with retardation and anticipation. This dissertation focuses on two sides:one is the basic theory of functional differential systems with retardation and anticipation, the other is the convergence theory of functional differential systems. The paper is made up of two chapters. In chapter one, we give a survey to the development and current state of functional differential systems with retardation and anticipation, as well as the main work status. In chapter two, A class of functional differential systems relative to both retardation and anticipation is investigated. By using monotone iterative technique, Ascoli-Arzela theory and Bellman inequality, constructing monotone sequences, obtain quadratic and rapid convergence of the sequences.