具分段常数变元的脉冲微分不等式与脉冲积分不等式

Impulsive Differential Inequalities and Impulsive Integral Inequalities with Piecewise Constant Arguments

本文研究了一类具分段常数变元的脉冲微分不等式。利用归纳和迭代法,得到了这类不等式解的有效估计。通过选择适当的变换,文中得到了若干具分段常数变元的脉冲积分不等式解的有效估计。最后,给出了该类不等式在脉冲微分系统振动性方面的应用。

In this paper, a class of impulsive differential inequalities is discussed. An efficient estimation for solutions of this kind of inequalities is derived by using induction and iteration. Moreover, some efficient estimations for solutions of impulsive integral inequalities are also obtained by proper transformations. Finally, an application for oscillation of impulsive differential systems is given to illustrate the inequalities.