Research On Periodic Solutions To Several Kinds Of Neutral Impulsive Differential Equations

Neutral differential equations are very popular functional differential equations and can be applied to many different fields. The phenomena of periodicity exist widely in natural science and social science, such as celestial mechanics, mechanical vibration, power systems, ecology, economics and so on. The effects of impulses can't be neglected. J.K.Hale and Zheng Zuxiu gave many examples with impulses, for instance, the mathematical model of high-speed computer connections without loss of the switch circuit transmission network is a neutral differential equation which has been used in many applications. If impulses are considered in this model, the existence and asymptotic behavior of periodic solutions are more meaningful.In this paper, several kinds of neutral impulsive differential equations are investigated. This paper is organized with four parts.In chapter I, we give a simple introduction of the development of neutral impulsive systems. Some methods which are widely used to deal with neutral impulsive differential equations are also introduced. In this chapter, we also give some necessary preliminaries and notions.In chapter 2, the existence of periodic solutions of a kind of neutral impulsive differential equation with forced termis considered. We consider several equations with constant impulses and obtain some sufficient conditions. When dealing with the impulsive differential equations with functional impulsive terms , we can turn them into the corresponding differential equations without impulses. There are widely valuable investigations of high order differential equations in neutral differential equations. Yan Jurang and other researchers have discussed in this field, however, they have not considered the effects of differential equations with impulses.In chapter 3, the existence of periodic solutions of a kind of higher-order nonlinear neutral differential equation with variable delaysis investigated. As is known, higher-order differential equations have more profound investigations and many scholars have special concerns on them. Yan Jurang also have many good works about them, but the results obtained by them are some of the differential equations without impulses.The existence of periodic solutions of neutral differential equations is investigated in chapter 2 and chapter 3. As far as I am concerned, the investigations on the asymptotic behavior of neutral differential equations are very necessary. There are many results of asymptotic behavior of differential equations with impulses, so, in chapter 4, the asymptotic behavior of a kind of neutral impulsive differential equationis considered and the results obtained extend some known results.