The Problems Of Periodic Pollution About Two Kinds Of Functional Differential Equation

Various kinds of problems have been mentioned in the field of nature science, such as in the fields of physics, biology, automatic control electrical technique, etc. meanwhile in the field of social science there are also some problems about functional differential equation. We usually set up mathematical model when solving actual problems. That is to say, a differential equation which reflects this actual problem has been formed. Then we use the solution to the equation to interpret the actual problem, as a result the actual problem has been solved.This article is aim to talk about two kinds of equations. In chapter 3, we use the theory of fixed point meds and Eigen value to talk about the problems of more time lay functional differential equation.We reached the following conclusion in article [1]:Theorem if the condition (H) and (P1) or (H) and (P2) are satisfied, then the periodic positive solutions of the equation (3.1.1) and (3.1.2) exists.In this chapter we obtain the theory of existence of periodic positive solutions of the equation. Moreover the theory of multiple positive solutions also has been gained. In the theory the continuity of every function is demanded in its deficient and it is about periodic function. The conclusions of this chapter are essentially extends the conditionThe conclusions of this chapter are essentially extends the condition (P1) and (P2) of literature [1] to the fist Eigen vale with respect to the relevant linear operator. In the end we use concrete birddog model to show the validity of studying the more time lay functional differential equation.In the chapter 4, we use inherent element theory to talk about the existence of periodic positive solution of singular time lay functional differential equationIn this thesis, we extend the parameters in the equation. Suppose condition (H1) and (H2) are satisfied to ensure the Green function is limitary. There by denture A is close and complete continuous. As application We study one kinds of singular time lay functional differential equation, and the plenitude condition is obtained to the existence of periodic positive solution.