Periodic Solutions For Several Kinds Of Functional Differential Equations

This thesis is composed of four chapters, which mainly studied the ex-istence and uniqueness of periodic solutions for one kind of neutral Volterra integro-differential equations with infinite delay,periodic solution for one kind of neutral Duffing equations and existence and multiplicity of positive periodic solutions for one kind of functional differential equations with impulses.As the introductions, in Chapter 1, the background and history of the existence and uniqueness or multiplicity of Periodicity solutions problems, and the main work of this paper are given.In Chapter 2, we studied the existence, uniqueness and stability of neutral Integro-differential equations By using the theory of exponential dichotomies of linear system and Schauder fixed point theorem, we obtain the existence and uniqueness theorem of peri-odic solutions for this kind of functional differential equations.In Chapter 3, we study a class of neutral Duffing equation, which have periodicity solutions ax"(t)+cx'(t-τ)+bx(t)+g(x(t-τ)))= p(t). By using the theory of coincidence degree, we obtain a sufficient theorem is obtained for the existence of a periodic solution of this kind of equations.In the last Chapter, we study the existence of multiple positive periodic solutions for functional differential equations with impulsesχ(t)= A(t,x(t))x(t)-λf(t-τ(t)),t≠Tk,k∈N x(τk+)=χ(Tk)+Ek(x(Tk)), t= Tk By using Krasnoselskii fixed point theorem, we obtain the existence of multiple positive periodic solutions for this kind of functional differential equations with impulses. Our results improve some known results or are new.