关键词: 脉冲积分方程, 脉冲积分-微分方程, 非紧性测度, 不动点

Abstract:

In this paper, under weak conditions, by useing the MÖnch fixed point theorem and the method of estimate step by step, some existence theorems of solutions for the nonlinear impulsive Volterra type integral equations in Banach space are proved. The results 
obtained improve and extend the known results. Then the authors give some applications to initial value problems for nonlinear impulsive first-order differential equations of mixed type in Banach space.

Key words: Impulsive integral equations, Impulsive integro-differential equations, Measure of noncompactness, Fixed point