Some Research On Periodic Solution Of Functional Differential Equations

Strictly speaking, in real life and production delay is inevitable, Even if information systems by transmitted at the speed of light is no exception. In this sense, the mathe-matical model, omitting delay is then not reach the necessary precision and even cause an error model. Therefore, the researches on functional differential equation have important theoretic value and practical significance.In this paper, the existence of the positive solutions or periodic solutions of several functional differential equations are discussed, many important results are also given in it. Full text is divided into five chapters.In the first Chapter, brief historical background and existing research of functional differential equations, focusing on the work of this study reviewed.In the second Chapter, we study two types of neutral functional differential equations with, finite or unbounded distributed deviating arguments. By using Banach contraction principle, we obtain some sufficient conditions for the existence of positive solutions to these equations.In Chapterâ…¢, using Mawhin's coincidence degree theory, the existence of the periodic solution of fourth-order differential equations are studied. Moreover, we construct an example to illustrate the feasibility of our results.In Chapterâ…£, using Krasnoselskii's fixed point theorem, Banach contraction prin-ciple, matrix measure and functional analysis methods, we study the existence of the periodic solutions of neutral differential equations with distributed and discrete delays. Moreover, we construct an example to illustrate the feasibility of our results.In chapterâ…¤, based on Manasevich-Mawhin continuation theorem and some analysis skill, some new sufficient conditions for the existence of periodic solutions for Duffing type p-Laplacian differential equation with several p-Laplacian operators are obtained. More-over, we construct an example to illustrate the feasibility of our results.