Periodic Problem Of The Impulsive Differential Systems

This paper discuss mainly the existence of positive solutions to periodic boundary value problems for first or second order impulsive differetial equations. In addition, impulsive differential equations applies to biological system, meanwhile, the optimal harvest policy with impulsive harvest is considered.This paper include most of research work when the author persue her Ph.D. degree.The whole contents is divided into five chapters.Chapter 1, as the beginning of this paper, offers some relative knowledge, such as preliminary qualitative theory of differential equation, basis theory of nonlinear functional analysis, theory of impulsive differential equation.Chapter 2, we obtained the existence positive periodic solutions of periodic boundary value problem for first order Lotka-Volterra integral differential equation with impulse effects and first order impulsive differential equation with delay. We mainly concerns the existence of the nonlinear continuous systems that have previously appeared in the population dyanmics literature such as single species logistic growth models, the model of blood cell production, and so on. New easily verifiable sufficient conditions are derived which improve and generalize related results.Chapter 3, Focuses on the existence positive periodic solution of periodic boundary problem for second order impulsive differential equation. As we all know the second order impulsive differential equation has much important physics significance to study. The method used here is alternative Leray-Schauder type and on the krasnosel-skii fixed point theorem, and studied the periodic solution of repulsive singular differential equation with impulse effects.Chapter 4, using the coincidence degree and the priori estimations, discuss the nonautonomous impulsive differential equations, including a predator-prey system and a cooperative systems.Chapter 5, combined the feasible principle, specially consider supposition of impulsive harvest and study sustainable development of biologic resources under the impulsive harvest, derive the existence and global asymptotically stability of impulsive periodic solution, furthermore, the optimal harvest policy is obtained. The classical re-suits of Clark's for the management of renewable biological resources are generalized. At the end of the paper, it is proposed the remark of this paper and the further study direction, many related references are listed.