Several Types Of Periodic Solution Of Functional Differential Equations States

This dissertation is mainly concerned with the existence of periodic solutions for some kinds of functional differential equations. This disser-tation is divided into five parts. First, the development of periodic solu-tions for functional differential equations and the degree theory and this paper's work are presented. In Chapter 2, the existence of periodic solu-tions of the Rayleigh functional differential equation is discussed. Based on the coincidence degree theory and related inequalities, some new suffi-cient conditions are given by which the relevant results have been signi-ficantly improved in existing literature. In Chapter 3, based on the coinci-dence degree theory and the theory of Fourier series, the existence of periodic solutions of the third-order functional differential equation is dis-cussed. Some new sufficient conditions on the existence of periodic solu-tion solutions are established. Chapter 4 describes a number of essential lemma, the existence of periodic solutions for the fourth-order nonlinear differential equation is studied by using the coincidence degree continua-tion theory and the more accurate priori estimates. Some sufficient condi-tions for the existence of periodic solutions for this kind of neutral func-tional differential equation are obtained under the weaker conditions, which improve and extend the relevant results in existing literature. In Chapter 5, based on the theory of coincidence degree and some analytical skills, the periodic solutions to a kind of high-order neutral functional differential equation with distributed delay is studied. Some sufficient conditions for the existence of periodic solutions for this kind of neutral functional differential equation are obtained under the weaker conditions, which improve and extend the relevant results in existing literature.