The Periodicity And The Boundary Value Problem Of The Differential Systems With Delays

This dissertation is composed of five chapters, which mainly investigated the existence and stability of periodic solutions for a class of delay differential systems, the existence of solutions for boundary value problems for singular differential systems with delays.In the first chapter, the preliminary knowledge which is necessary in the paper is given. The basic concepts of matrix pencil, the Drazin inverse, Fred-holm mapping, Continuation theorem, Arzela-Ascoli theorem and matrix measure are introduced.In the second chapter, we study the existence and stability of periodic solutions for a class of delay differential systems. And for the first place we study the existence and stability of periodic solutions for a class of differential systems with piecewise continuous delays. By using continuation theorem of the coincidence degree theory, some sufficient conditions are obtained. And by using the Liapunov functional method, we study the uniqueness and globally asymptotic stability of periodic solutions.In chapter 3, by using continuation theorem of the coincidence degree theory and some analysis techniques, we study the existence and globally asymptotic stability of periodic solutions for a class of delayed neural networks.Chapter 4 mainly considers the periodicity for singular differential systems with delays. By using Krasnoselskii fixed point theorem, some sufficient conditions for the existence of periodic solutions are obtained.In the last chapter, by using the Schauder fixed point theorem, we give a sufficient condition for the existence of solutions for boundary value problems...