Research On Periodic Solution For Some Classes Of Third Order Functional Differential Equations With Delays

Functional differential equation is a mathematical model describing the phe-nomenon with time delays.The functional differential equations with periodic delays represent a natural framework for mathematical modeling of many real world phe-nomena such as biology, economy, ecology, the population dynamic system and so on.Therefore, the researches on existence and uniqueness of periodic solutions for functional differential equations with periodic delays have practical significance.This paper mainly discusses the problems on existence and uniqueness of peri-odic solutions for some classes of three order functional differential equations with delays. The full text is divided into five chapters.In chapter Ⅰ, the background knowledge of the subjects relevant to this dis-sertation and the study of dynamic are introduced.Then, the main results of the thesis are introduced.In Chapter Ⅱ,using the theory of coincide degree,a type of third order func-tional differential equation with delays is considered.Some new results on the existence and uniqueness of periodic solutions are obtained.In Chapter Ⅲ,using the theory of coincide degree,on the based of the second chapter,a type of third order functional differential equation with more delays is considered.Some sufficient conditions that guarantee the existence and uniqueness of periodic solution of the equation are obtained.In Chapter IV,comparing the fourth chapter,a different research methods is used to study this equation.Specifically,using the continuation theory for K-set con-tractive operator,a type of third order functional differential equation with more delays is considored.The sufficient conditions for the existance of unique T-periodic solution are obtained.In Chapter V,by using continuation theorem in coincidence degree theory, a type of third order p-Laplacian Equation with a deviating argument ((φp((x(t)-cx(t-σ))"))’+f1(x(t))x’(t)+f2(x’(t))x"(t)+g(t, x(t), x(t-τ(t)),(?)x(t+s) dm(s))=e(t) is considered.The sufficient condition for the existance of T-periodic solution is obtained.