Existence Of Periodic Solutions For Two Kinds Of Nonlinear Neutral Differential Functions Equations

The dissertation is most concerned with the existence of periodic solutions for two kinds of nonlinear neutral functional differential equations, by using the Krasnoselskii fixed point theory and coincidence degree theory. This dissertation is divided into three main chapters.First of all, Chapter1, the development of periodic solutions for functional differential equations, specially, nonlinear neutral differential equations are introduced briefly, then the Krasnoselskii fixed point theory, the degree theory of Coincidence Degree Theory are also introduced.The main conclusions of this work are surveyed.Chapter2is devoted to studying a class of second order nonlinear neutral functional differential equations as following:Using the Krasnoselskii fixed point theory, the existence of periodic solutions are obtained. Some new sufficient conditions are given which the relevant part of results have been significantly improved in relevant existing literature.Chapter3is concerned with a class of nonlinear neutral functional differential equation of high order as following:[x(t)+cx(t-τ)](n)+f(t,x(t),x’(t),…x(n-1)(t))+g(t,x(t-γ(t)))=p(t)By using the Continuation theorem of coincidence degree theory, the existence of T periodic solutions are obtained.