Banach空间中二阶非线性脉冲微分积分方程初值问题的整体解

通过逐步求解,应用Banach不动点定理,在较宽松的条件下,获得Banach空间中二阶非线性脉冲微分积分方程初值问题解的存在性与唯一性及解的迭代逼近.对文［1］的结果及文［2］相应于d-0=0的结果,作了重要改进和推广.

Initial Problems for Nonlinear Second Order Impulsive Integro differential Equation in Banach Space

Through solving the problem step-step and by applying Banach fixed-point theorem, under simple conditions, the author has obtained existence and uniqueness and iterative approximation of solution for initial value problems of nonlinear second order impulsive integrol-differential equations in Banach space, and improved and generalized the corresponding results of [1] and [2] for d-0=0. Moreover, the method is different essentially from those in [1],[2].