Periodic Solutions And Periodic Boundary Value Problems Of Functional Differential Systems

During the past several years, wide attentions have been paid to the delaysystems and impulsive periodic systems by many scholars due to their deeplypractical backgrounds. And many good results have been obtained in differ-ent fields. Furthermore, delay, impulse and period are existing universally inengineering, economy, biology, etc.. So we have to take the influence of impulseand delay into account if describing many systems more accurately in manypractical problems. Then it is meaningful for us to study the characters ofperiodic solutions of infinite delay and impulsive delay functional differentialsystems.In this paper, the existence of periodic solutions and periodic bound-ary value problems of infinite delay and impulsive delay functional differentialequations are studied. And it is mainly composed of four chapters.In chapter one, the backgrounds and significance of the problems are given.The main work done in this paper is introduced.Chapter two mainly discusses the existence of positive periodic solutionsfor infinite delay functional differential equations.And we also give the relevanttheorems and specific examples.In chapter three, by ultilizing the continuation theorem in coincidencedegree, we have obtained the conditions of the existence of positive periodicsolutions for a kind of neutral multi-species functional differential equationswith impulsive delays.In the last chapter, by using a fixed point theorem on cone in Banachspace, we disseuss the positive solutions for a kind of second-order two-point periodic boundary value problems, and some existence results of positive so-lutions are established.