Banach空间一阶脉冲积分-微分方程及其应用

One-order Impulsive Integro-differential Equation in Banach Spaces and Its Applications

首先,考虑Banach空间一阶脉冲积分-微分方程,利用Mnch不动点定理和一个比较不等式,证明了其初值问题解的存在性。随后,将这一结果应用于右端项含有导数的二阶脉冲积分-微分方程,获得了其解存在性的一个新结果。

First, by the fixed point theorem and an inequality, the first order impulsive integro-differential equation in Banach spaces is considered and the existence of its solutions is obtained. The application of it to the second order impulsive integro-differential equation with a derivative in its right item in Banach spaces comes to a new conclusion about the existence of solutions of the problem.