Banach空间不连续的脉冲微分-积分方程的解与迭代解  

Solutions and Iterative Solutions of Discontinuous Impulsive Integro-Differential Equations in Banach Spaces

作　　者：刘笑颖[1] 吴从炘[1] 

机构地区：[1]哈尔滨工业大学数学系

出　　处：《数学学报（中文版）》2001年第3期469-474,共6页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(19971019)

摘　　要：本文通过建立一个比较结果，应用不动点定理与上、下解方法，讨论了Ｂａｎａｃｈ空间含间断项的一阶混合型脉冲微分－积分方程初值问题的最大解和最小解，并在非线性项满足Ｃａｒａｔｈｅｏｄｏｒｙ条件时获得了解的迭代，推广改进了某些文献中的相应结果．By establishing a comparison result and using the fiXed point theorem and the method of the upper and lower solutions, the maximal and minimal solutions of the initial value problem for the first order impulsive integro-differential equations of mixed type with discontinuous terms in Banach spaces are investigated. In the case that the nonlinearity satisfies the Caratheodory condition, we obtain the successive approximation of solutions. Our results improve and generalize those in some wellknown papers.

关 键 词：不连续初值问题 脉冲微分-积分方程 Banach空间 解 不动点定理 迭代 CARATHEODORY条件 最大解 最小解 

分 类 号：O175.8[理学—数学] O175.6[理学—基础数学]