Boundary Value Problems For Impulsive Differential Equations And Permanence For Impulsive Model

This thesis mainly studies the existence of solutions for impulsive boundary value problems and permanence and extinction for impulsive model. It is consisted of five chapters.As the introductions, in Chapter 1, the background and history of boundary value problems and mathematical model with impulsive effect are briefly addressed, and the main work of this paper is given.In Chapter 2, we focus on the existence of solutions for two class of impulsive differential equations with nonliear boundary conditions. By using an impulsive differential inequality, we obtain a comparsion result on a impulsive three-point boundary value problems, and using the method of upper anf lower solutions coupled with monotone iterative technique,we obtain the existence of extremal solution about three-point boundary value problems. In the view of the existence of upper and lower solutions, by using Schauder fixed point theorem and the method of a priori estimates, we obtain existence result about two-point boundary value problems.Chapter 3 concerns positive solution of impulsive periodic boundary value problem and singular impulsive boundary value problem. Using fixed point theorem on cone, we give the sufficient conditions for the existence of positive solutions without assuming the existence of positive solutions of the corresponding continuous equation. By using degree theorem and the method of a priori estimates, we obtain the existence results for singular boundary value problems which admites that function f(t, u, u') may be sinluar at u = 0 or u' = 0.In chapter 4, we consider the permanence and the existence of positive periodic solution for impulsive model with Holling type III functional response. We find that the criteria for the permanence is exactly the same as that for the existence of positive periodic solutions.In chapter 5, we discuss the permanence and extinction for two class of two dimensional impulsive competitive model. We obtain several conditions guaratee- ing that one species will be driven to extinction while the other will stabilize at a certain solution of a impulsive logistic equation.