The Existence Of Periodic Solutions For Several Types Of Neutral Functional Differential Equations

In this master dissertation, the existence of periodic solutions for some kinds of neutral functional differential equations is considered, and the sufficient conditions of existence of periodic solutions are obtained. These results have important theoretical significance and wide range of applications. This dissertation is divided into three parts.Chapter1is an overview section. At first, the historical background and the basic theory of the development of neutral functional differential equations are briefly introduced. By the definition of differential difference equations and differential integral equation, we introduce the definition of the functional differential equation and the neutral functional differential equations. In addition, the preliminary knowledge and main results of this thesis are presented.In Chapter2, a class of third order more general p-Laplacian neutral equation, a class of fourth order of p-Laplacian neutral equations and a class of fourth order p-Laplacian equation with deviating arguments are studied. By coincidence degree theory, theorems of the existence of periodic solutions for these p-Laplacian neutral functional differential equations are established.In Chapter3, we mainly discuss the existence of periodic solutions for a class invariant coefficient and a kind of variable coefficient higher order neutral functional differential equation.