Banach空间中二阶脉冲积分微分方程解的存在性

Existence of the Solutions for the Second Order Impulsive Integro-Differential Equations in Banach Space

利用一个非线性压缩型不动点定理,讨论了Banach空间中二阶非线性脉冲积分 微分方程解的存在性.改进和推广了GuoDajun,SunJinli和MaYihai的工作,并且仅需要压缩条件,去掉了SunJinli和MaYihai的工作中使用的单调性条件.

The paper studys the existence of the solutions for second order impulsive integro-differential equations in Banach space by using fixed point theorems. The results improve the some results obtained by Dajun Guo, Jinli Sun and Yihai Ma. Besides,the results greatly simplify the proof of Jinli Sun and Yihai Ma. Based on our results, there is only need for the contraction conditions, but no need for any monotone condition used by Jinli Sun and Yihai Ma.