序Banach空间中不连续脉冲积分-微分方程初值问题的解

SOLUTION OF DISCONTINUOUS IMPULSIVE INTEGRO-DIFFERENTIAL EQUATIONS IN ORDERED BANACH SPACES

讨论了序Banach空间不连续脉冲积分.微分方程初值问题,通过建立一个新的比较定理,在比较弱的条件下推广了相关文献的主要结果.并在比较广泛的上控制条件而且只有一个上解或下解的假设下,获得了唯一解的存在性定理,而且给出了迭代序列的误差估计.从而推广并改进了最近某些文献中的相应结果.

In this paper, the initial value problem for first order discontinuous impulsive integro-differential equations in ordered Banach spaces is investigated. By establishing a new comparison theorem and using only an upper or lower solution, the unique solution for the first order impulsive integro-differential equations can be obtained. The error estimate of the iterative sequences of approximation solutions is given. The results generalize and improve the corresponding results in some recent well-known papers.