一阶脉冲微分方程解的存在性及稳定性

Existence and stability of one-order impulsive differential equation

脉冲微分方程广泛地应用于理论力学、化学、生物学、医学、控制理论等诸多学科领域.近年来脉冲泛函微分方程解的存在性及稳定性的研究受到了越来越多的研究者的重视,普遍的方法是利用李亚普诺夫泛函方法和比较方法.利用迭代分析方法获得了一类非线性脉冲微分方程解的存在性和稳定性,结果表明,所讨论问题的解与时滞变量和脉冲条件密不可分.

Impulsive differential equations can be successfully used for mathematical simulation in theoretical physics,chemistry,biotechnology,medicine,population dynamics,optimal control,and in other processes and phenomena in science and technology.The stability theory of impulsive differential equations has been developed by a large number of mathematicians,and their studies have attracted much attention.They have been successful in different approaches based on Lyapunov direct method and comparison technique.In this paper,we employ the iterative method which is very concrete to obtain the existence and stability of one kind of impulsive differential equation.From the discussion in the paper,we can see that the stabilities of the problems which are all connected with the impulsive condition and delay variables closely.