序Banach空间不连续脉冲积分-微分方程初值问题的解

王增桂;刘立山

系统科学与数学 ›› 2008, Vol. 28 ›› Issue (2) : 197-207.

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系统科学与数学 ›› 2008, Vol. 28 ›› Issue (2) : 197-207. DOI: 10.12341/jssms10059
论文

序Banach空间不连续脉冲积分-微分方程初值问题的解

    王增桂,刘立山
作者信息 +

Solution of Discontinuous Impulsive Integro-Differential Equations in Ordered Banach Spaces

    WANG Zenggui, LIU Lishan
Author information +
文章历史 +

摘要

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.

Abstract

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.

关键词

序Banach空间 / 初值问题 / 不连续脉冲积分-微分方程 / 唯一解.

Key words

Ordered Banach spaces / initial value problem / discontinuous impulsive integro-differential equations / unique solutions.

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王增桂 , 刘立山. 序Banach空间不连续脉冲积分-微分方程初值问题的解. 系统科学与数学, 2008, 28(2): 197-207. https://doi.org/10.12341/jssms10059
WANG Zenggui , LIU Lishan. Solution of Discontinuous Impulsive Integro-Differential Equations in Ordered Banach Spaces. Journal of Systems Science and Mathematical Sciences, 2008, 28(2): 197-207 https://doi.org/10.12341/jssms10059
中图分类号： 34B15    34B25   
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