The Existence Of Periodic Solutions For Two Kinds Of High Order Differential Equations With Deviating Arguments

Functional differential equation is a mathematical model describing the phenomenon with time delays. The functional differential equations with periodic delays represent a natural framework for mathematical modeling of many real world phenomena such as biology, economy, ecology, automatic control and so on. Therefore, the researches on existence of periodic solutions for functional differential equations with periodic delays have practical significance.Furthermore, investigating periodic solution problem for functional differential equation not only has applied value but also enriches the system of functional differential equation.This thesis mainly studies the periodic solution problem for functional differential equations, as following:In chapterâ… , 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 chapterâ…¡, we study a kind of periodic solutions of the second order differential equation with multiple deviating arguments is investigated.By means of Mawhin continue theorem and sharp inequalities for periodic functions, some sufficient conditions are obtained.In chapterâ…¢, we study a kind of third order functional differential equation with a deviating argument is investigated. Sufficient conditions for the existence of periodic solutions are obtained.