一阶脉冲微分方程脉冲聚点的存在性条件

Existence of Pulse Accumulation Point for First-order IDE

针对一阶时变脉冲微分方程初值问题脉冲聚点的存在性问题,首先证明了比较原理见引理2和引理3,其次研究了解x(t)与某些曲面Sk相遇无限多次的情形,并在相对较弱的条件下建立了依赖状态的脉冲微分方程脉冲聚点存在的充分条件,得到的相应结论推广了已有结果。

In the paper existence of pulse accumulation point for initial value problem of first-order impulsive differential equations with variable times was disscused. Firstly the comparison principle was proved, that is lemma 2 and lemma 3. Secondly the problem of the solution x（t） hits the surface Sk infinite times was studied, and the sufficient conditions of the existence of pulse accumulation point for impulsive differential equations under weak conditions was obtained. The results extend and improve the previous results.