The Study Of Properties Of Solutions For Several Kinds Of Differential Equations On Time Scales

The theory of measure chain can help to avoid proving the differential equations and difference equations and it provides insight into the relationship between them.It has great significance in theory and applications.And Volterra system and predator-prey system are an important content of population dynamics.This model is extensively applied in ecological balance.In the paper,the existence and stability of solutions for dynamic equation(s)on measure chains are studied.In this paper,the existence and stability of solutions for differential equation(s)on time scales are studied.We obtain some sufficient conditions the stability of the zero solution of Volterra integral equation,and obtain the the existence of periodic solution for two kinds proposed predator-prey system with a predator and the stronger and weaker prey on time scales.The paper is organized in six chapters.In chaper 1,we give the background and some basic theories for differential equation(s)on time scales.We recall some known results and briefly make a describtion on our main work in the present paper.In chaper 2,we consider the stability of the zero solution of a kind of Volterra integral equations with respect to two classes of bounded perturbations on time scales.By using Lyapunov direct method and some inequality techniques,some sufficient conditions for the stability of zero solution for the model were established on time scales.In chaper 3,with the help of continuation theorem based on the Gaines and Mawhin coincidence degree theory,we investigate the existence of periodic solution for two kinds proposed predator-prey system with a predator and the stronger and weaker prey on time scales.Meanwhile we also respectively obtained some sufficient conditions for two kinds predator-prey systems with a predator and the stronger and weaker prey on time scales.In Chapter 4,we give a summary and the outlook of this thesis.