Existence And Uniqueness Of Periodic Solutions For Differential Equations With Delays

The periodic solutions of differential equations have very important meaning of theory and practice. In this paper, by using the continuity theorem in coincidence degree theory and Lyapunov functional method, we deal with the existence and the uniqueness of the the periodic solutions of a class of differential equations with delays. By applying the theory of exponential dichotomy of linear system and Krasnoselskii's fixed point theorem, we obtain some sufficient conditions that guarantee the existence of the periodic solutions of a class of neutral periodic differential equations.The tree of this paper is as follows:In chapter 1, using the continuity theorem in coincidence degree theory, we study the existence of the periodic solution of the following periodic system:More general results are obtained, which genralize the relation results in [9,18]. Main results:Theorem 1.1 : Suppose that there exist positive constants CJ, d_j(j = 1,2,... ,p),δ, e, /, and continuous functions h(s},s∈[—r", 0], satisying : h(s)≥O.Ifτtj(t) < l,T/(t) < 1 and a > cjkj hold , and for any (t,x) e [0,ω] x Rnthe following conditions hold:(1)|g_j(t,x)|