The Study Of Qualitative Properties Of Solutions Of Delay Differential Equations

Differential equations is an important branch of modern mathematics. With the development of modern society, differential equations is widely used in engineering astronavigation, economy, financial etc. In most cases, many problems are solved more practically by delay differential equations than ordinary equations great achievements have been given by the respective researchers. At the same time, the scholars are studying the basic theories and the qualities theories on delay functional differential equations. On one hand, the research enrich and develop the theory of delay differential equations, on the other hand, the necessary theoretical basis is given the practical application.In this paper, we study the existence of periodic solutions for delay differential equations, the delay differential systems in a Banach space and the existence, uniqueness and global attractivity of solutions for some delay differential equations.The article encompassing five chapters is divided into three main parts. The second and the third chapter constitute part I, which deal with the existence of periodic solutions for delay differential equations. By using the method of coincidence degree, a set of easily verifiable sufficient condition are derived for the existence of at least one or two positive periodic solution. Some new results are obtained here. The part II is composed of the fourth chapter. The purpose of this part is to study the delay differential systems in Banach space using the method of fixed point theorem. And the part III is composed of the fifth chapter. In this part, we study a class of integral equations.