Boundary Value Problems And Periodic Solutions Of Impulsive Differential Equations

This thesis mainly studies the existence of solutions for impulsive boundary value problems, the existence and global asymptotically stability of positive periodic solutions for impulsive predator-prey model with disperion and time delays, and the periodicty and boundednees in impulsive functional differential equations with finite and infinite delays. It is consists of four chapters.As the introductions, in Chapter 1, the background and history of boundary value problems and periodicty for impulsive differential equations are briefly addressed, and the main work of this paper are given.In Chapter 2, by using an impulsive differential inequality, we obtain a new comparison result on an 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 this problems. By using the nonlinear alternative of Leray-Shauder type, the Leray-Shauder continuation theorem, the method of a priori estimates and a diagonalization argument, we study the existence of solutions for impulsive boundary value problems on infinity intervals and initial value problems with singular, and some sufficient conditions be given. Our results improve some known results or are new.Chapter 3, mainly considers an impulsive predator-prey model with dispersion and time delays. The existence of positive periodic solution is obtain by the help of Mawhin continuation theorem and coincidence degree theory and the global asymptotically stability of positive periodic solution is presented by Lya-punove method and Barbalat's theorem.In Chapter 4, by means of Horn's theorem, under the assumption that solutions are uniformly bounded and uniformly ultimate bounded, we investigate the existence of periodic solutions for impulsive functional differential equations with finite and infinite delays, and some sufficient conditions are established. By Lyapunove method, we obtain some sufficient conditions for solutions uniformlybounded and uniformly ultimate bounded.