Periodic Solutions For Some Kinds Of Functional Differential Equations

This thesis contains three chapters.In the first chapter ,by using the theory of exponential dichotomy and some fixed-point theorms,we discussed the nonlinear functional differential equationx'(t) = A(t, x(t - r(t)))x(t) + f(t, x(t - r(t)))and obtained several new results about the existence of periodic solutions which extended the related results in [4] and [5].In Chapter two, the existence of periodic solutions for a third-order functional differential equationwas discussed by applying the coincidence degree. The result in [18] was extended.In the last chapter, we employed the same approach adopted in Chapter two to study the nonautonomous planar systemsA sufficient condition for the existence of non-constant periodic solutions was obtained, which extended the result in [28]on autonomous systems .