The Existence Of Periodic Solutions Of Several Kinds Of Functional Differential Equations

This paper consists of five chapters. In Chapter 1, we state the historical status of the existence of periodic solutions of several kinds of functional differential equations and two classes of continuation theorems of coincidence degree theory regarding the paper. In Chapter 2, we study the existence of periodic traveling waves in systems of a kind of reaction diffusion equations with delays and for the first place give the existence results of periodic traveling waves of the above system with delays by mean of establishing the existence conditions of periodic solutions of its corresponding traveling wave equations. In Chapters 3 and 4, we investigate the existence of periodic solutions of a class of second order functional differential equation and a class of third order functional differential equation, respectively, and obtain new sufficient conditions of their existence result of periodic solutions under growth conditions and linear growth condition, respectively. Compared with some known results in the literature, the equations discussed by us are more general, and our results are concise and easy to be verified. In Chapter 5, we first investigate the existence of periodic solutions of a food chain system and give the existence results of periodic solutions for this system. Then, we investigate the existence of periodic solutions of two classes of predator-prey diffusive systems and obtain the existence results of positive periodic solutions for two kinds of predator-prey diffusive systems.