Periodic Solutions Of Functional Differential Equations With Infinite Delay

This thesis is concerned with the existence of periodic solutions of functional differential equations with infinite delay. The thesis contains four chapters.Chapter 1 introduces the research background, preliminaries, notion of some matrix measures and the axiom systems of phase spaces.Chapter 2 deals with periodic solutions of a class of functional differential equations with infinite delay. Some existence results on periodic solutions are established for functional differential equations with infinite delay by using matrix measure and Leray — Schauder fixed point theorem.Chapter 3 discusses positive periodic solutions for a class of second order functional differential equations with infinite delay. Some existence and multiplicity results of positive periodic solutions are derived by utilizing the fixed point theorem on the abstract cone. An example is given to illustrate the main results.Chapter 4 studies positive periodic solutions for a class of second order neutral functional differential equations with infinite delay. Under the suitable conditions, the existence of positive periodic solutions is established by utilizing Banach fixed point theorem.