The Periodic Solution And Almost Periodic Solution Of Degenerate Differential Equation With Delay

Degenerate differential system with delay as an effective method of emulating models in realistic world have aroused the notice of mathematicians. In the course of practical systems emulation, design, analysis and application research, people found that there were many degenerate and time delay phenomena existing in many practical fields such as industrial project system, power system, ecosystem, financial system and so on, so that many scholars have research the system with degenerate and delay systematically and made comprehensive progress, Particularly, many systematic results[l-30] have been obtained on the studying of periodic solutions and almost periodic solutions of the degenerate differential system with delay. However, many more complex mathematics models( as: Biological mathematics artificial nerve network) research show that Current period systematic theory need to be improved further. And in the paper, the periodic solution and almost periodic solution of the degenerate differential systems with delay are discussed and many important results are also given in it.There are four chapters in this paper.In the first chapter, the preliminary knowledge which is necessary in the paper is given. The basic concept of exponential dichotomies of linear system and matrix measure are given.In chapter 2, By combining the theory of exponential dichotomies of linear system and the method of functional analysis, some sufficient conditions that guarantee the existence and uniqueness of periodic solution of the systems are obtained.