Banach空间非线性二阶混合型脉冲积分-微分方程的解

Solutions of Nonlinear Second Order Impulsive Integro-Differential Equations of Mixed Type in Banach Spaces

利用Mnch不动点定理以及一个脉冲积分不等式,研究二阶混合型脉冲积分-微分方程初值问题解的存在性.结果涉及右端项既包含导数又包含积分算子Sx的情形.最后给出了一个应用例子.

In this paper, by the Monch＇s _fixed point theorem and an impulsive integral inequality, we establish the existence of solutions of initial value problems for nonlinear second order impulsive integro-differential equations of mixed-type in Banach spaces. It is desirable that our results involve the right item f with both the derivative and the linear integral operator Sx. An example is given to demonstrate our result.