Periodic And Anti-periodic Solutions Of Several Kinds Of Functional Differential Equations

This master's degree thesis mainly deals with existence of periodic solutions and anti-periodic solutions for several kinds of functional differential equations.The main tools are Krasnoselskii fixed point theorem,contracting mapping principle,Schauder fixed point theorem,the upper and lower solution method,Leray-Schauder degree theory and some analysis techniques.The organizational structure of this paper are as follows:In the first chapter,a brief introduction to the developments of the periodic solutions and the anti-periodic solution and some relevant research backgrounds are presented.In the second chapter,using the Krasnoselskii fixed point theorem and Banach con-tracting mapping principle,existence of anti-periodic solutions of two classes of neutral functional differential equations are obtained,and improved the existing conclusions.In the third chapter,using the upper and lower solutions method and Schauder fixed point theorem,existence results of ?-periodic solution and multiple periodic solutions of a class of nonlinear neutral functional differential equation are obtained.In the fourth chapter,using the theory of Leray-Schauder degrees,a class of higher or-der and second order nonlinear delay Rayleigh equation are studied.Some fine conclusion on the existence and uniqueness of periodic solutions of above equations are established,which extends the existing results.