Research On Anti-Periodic Solution And Periodic Solution For Sevral Kinds Of Higher Order Of Functional Differential Equations

Functional differential equation is a mathematical model describing the phe-nomenon with time delays. The functional differential equations with anti-periodic delays and periodic delays arc playing a important role in mathematical modeling of many real world phenomena such as biology, economy, ecology, the population dynamic system and so on. For example, impulse cellular neural networks, an-imal blood red cells model, population dynamic system model,Infectious disease dynamic model,engineering,power, ecology, the financial system model and other models. Therefore, the researches on existence and uniqueness of anti-periodic solu-tions and periodic solutions for functional differential equations with anti-periodic delays and periodic delays is more realistic.Therefore, it becomes of great importance to study on the existence and unique-ness on anti-periodic solutions and periodic solutions of Functional differential equa-tion. Moreover, research on anti-periodic solution or periodic solution for functional differential equation not only has application value, but also enriches the system of functional differential equation.This thesis mainly studies on the anti-periodic solution and periodic solution problem for functional differential equations,Concrete structure as follows:In chapterⅠ, the background of the subjects relevant to this dissertation is introduced. Then, the known progress on study of functional differential equation and the main results of the thesis are introduced.In ChapterⅡ, a kind of n order functional differential equation with multiple delays and distributed delays is investigated. By means of the theory of Leray-Schauder degree and some new analysis skills, some sufficient conditions are ob-tained to ensure the existence and uniqueness of anti-periodic solutions of the sys-tem. Moreover, an example is given to illustrate the effectiveness of our results. In ChapterⅢ, a class of p-Lapcaian neural functional differential equation with multiple delays is discussed. By Leray-Schauder fixed point theorem and some new analysis skills,some sufficient conditions are obtained to ensure the existence of anti-periodic solutions of the system. our results are novel and promote the conclusions of the previous reference known results. Moreover, an example is given to illustrate the effectiveness of our results as an application of the theorem.In ChapterⅣ, by using the theorem of Mawhin Continuation theorem and some new analysis skills,the theorem of the proof is divided into four steps.we in-vestigate the existence of periodic solutions for a fourth-order p-Lapcaian neural functional differential equation.