Boundary Value Problems And Periodic Solutions Of Impulsive Differential Equations

This thesis mainly studies the existence of minimal and maximal solutions of the periodic boundary value problem for first-order impulsive functional differential equations,the existence of nonlinear boundary condition solutions for the integro-differential equations with impulsive,and the existence of positive periodic solutions for impulsive predator-prey model with disperion and time delays. It is consisted of four chapters.In Chapter 1, which serves as the introduction, the background and history of boundary value problems and periodicty for impulsive differential equations are briefly addressed, and the main work of this paper is given.In Chapter 2, by means of the method of upper and lower solutions and the monotone iterative technique, the existence of extremal solution about this problems are obtain. The results improve some results in [21].In Chapter 3, the existence of nonlinear boundary condition solutions for the integro-differential equations with impulsive are considered. By employing the monotone iterative method, some results are given.In Chapter 4, an impulsive predator-prey model with dispersion and time delays are mainly considered. The existence of positive periodic solution is obtained with the help of Mawhin continuation theorem and coincidence degree theory.