The Study About The Properties Of Solution For Several Kinds Of Differential Equations

In this paper, we investigate several kinds of ordinary differential equations, some sufficient conditions for the existence of positive bounded ,almost periodic, periodic solution of these systems are obtained. Moreover, some properties of exponential dichotomy on linear system are generalized to that of generalized exponential dichotomy. The thesis is composed of three parts.In Part 1, we consider linear systemBy using traditional methods of combining analysis and algebra, we obtained some properties of generalized exponential dichotomy of linear system. our results generalize those ones in [1,2,23].Moreover, we proposed a criteria to guarantee the existence of generalized exponential dichotomy for a class of linear systemThus we generalize the results of [13].In Part 2,we investigate a class of bidirectional associative memory (BAM) networks with distributed delaysBy using the theories of exponential dichotomy ,contraction mapping and almost periodic differential equations, we obtain sufficient conditions for the existence and uniqueness positive of bounded solution and almost periodic solution, respectively.In Part 3 we study the mutualism system with several delaysSufficient conditions are obtained for the existence of positive periodic solutions of the system by using the theory of Mawhin coincidence degree .