Banach空间中一阶非线性脉冲积分-微分方程初值问题

张晓燕

系统科学与数学 ›› 2010, Vol. 30 ›› Issue (12) : 1695-1703.

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系统科学与数学 ›› 2010, Vol. 30 ›› Issue (12) : 1695-1703. DOI: 10.12341/jssms09444
论文

Banach空间中一阶非线性脉冲积分-微分方程初值问题

    张晓燕
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Initial Value Problems of Nonlinear First-Order Impulsive Integro-Differential Equations in Banach Spaces

    ZHANG Xiaoyan
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摘要

通过引入函数e−λt\ (其中λ>0是一给定的常数)和分段利用M\"{o}nch不动点定理,在非常弱的条件下,建立了Banach空间中一阶非线性脉冲积分-微分方程初值问题整体解的存在性,改进和统一了已有的最近结果.

Abstract

In this paper, under rather weak conditions, we establish the existence of global solutions of the initial value problem for nonlinear first-order impulsive integro-differential equations of mixed type in Banach spaces is established by introducing the function e−λt\ (where λ>0 is a given constant) and by using M\"{o}nch fixed point theorem on each interval. The results improve and unify the recent existing results.

关键词

非线性脉冲积分-微分方程 / 初值问题 / 非紧性测度 / 整体解 / M\"{o}nch不动点定理.

Key words

Nonlinear impulsive integro-differential equations / initial value problem / measure of noncompactness / global solution / M\"{o}nch fixed point theorem.

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张晓燕. Banach空间中一阶非线性脉冲积分-微分方程初值问题. 系统科学与数学, 2010, 30(12): 1695-1703. https://doi.org/10.12341/jssms09444
ZHANG Xiaoyan. Initial Value Problems of Nonlinear First-Order Impulsive Integro-Differential Equations in Banach Spaces. Journal of Systems Science and Mathematical Sciences, 2010, 30(12): 1695-1703 https://doi.org/10.12341/jssms09444
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