时变脉冲微分方程初值问题解的存在性

Existence of solutions to initial-value problem of impulsive differential equations with variable times

首先给出了脉冲微分方程初值问题的解与相对应的常微分方程初值问题的解之间的关系,然后利用常微分方程理论讨论了一类时变脉冲微分方程初值问题,并在相对较弱的条件下建立了解的存在性定理,所得解允许和某些Sk相遇多次,推广了相关问题的已有结果.

First, the relations between solutions of initial-value problems for impulsive differential equations and solutions of initial-value problems for the corresponding ordinary differential equations were considered. Then, the theory of ordinary differential equations was employed to discuss a class of initial-value problems of impulsive differential equations with variable times, and some results of existence of solutions to it were established under relatively weaker conditions. The solution obtained permitted of repeated hit against several Sk. Some known results were extended and improved.