Existence Problems Of Solution For Impulsive Differential Systems

This thesis mainly studies the existence of periodic solutions and boundary value problems for impulsive differential equations,the existence and global attractivity of positive periodic solutions for impulsive predator-prey model with disperson and time delays.It is consists of five chapters.As the introductions,in Chapter 1,the background and history of periodicity and boundary value problems for impulsive differential equations are briefly addressed,and the main work of this paper are given.Chapter 2 concerns the existence of solutions for impulsive differential equations with periodic boundary value.By using an impulsive differential inequality and analysis technique,we obtain some new comparison results on a first order impulsive periodic boundary value problems,and using the method of upper and lower solutions coupled with monotone iterative technique,we obtain the existence of extremal solution about periodic boundary value problems.Meanwhile, we recorrect the wrong comparison result of second order impulsive periodic boundary value problems in the previous paper,and present new definitions of upper and lower solutions.In chapter 3,we discuss the existence of solutions for impulsive differential equations with two-point boundary condition.In the view of the existence of upper and lower solutions,by using Leray-Schauder degree theory,we obtain the existence result and multiplicity of solutions about two-point boundary value problems. By mean of five functionals fixed point theorem,we establish the existence of at least three positive solutions of boundary value problems for p-Laplacian impulsive functional dynamic equations on time scales.In Chapter 4,we consider the existence of positive periodic solutions for impulsive differential equations with a parameter.Converting it to non-impulsive differential equation and using Krasnoselskill's and Leggett-Williams fixed theorems, we obtain that the existence and amount of positive solutions is concerned with the parameter.Especially,we establish sufficient conditions for the existence of triple positive periodic solutions.In Chapter 5,we focus on an impulsive predator-prey model with dispersion and time delays.The existence of positive periodic solution is obtained by the help of Mawhin continuation coincidence degree theory and the global attractivity of positive periodic solution is presented by Lyapunove method.