一阶线性脉冲微分方程初值问题的有界变差解  

Bounded Variation Solutions to Initial Value Problems for the First Order Linear Impulsive Differential Equations

作　　者：李宝麟[1] 李林强[1] 

机构地区：[1]西北师范大学数学与信息科学学院,兰州730070

出　　处：《工程数学学报》2011年第6期832-838,共7页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(11061031);甘肃省555创新人才工程项目(GS-555-CXRC);西北师范大学科技创新工程项目(NWNU-KJCXGC-212)~~

摘　　要：本文利用广义常微分方程理论,讨论了广义线性常微分方程和一阶线性脉冲微分方程之间的关系,得到了一阶线性脉冲微分方程初值问题有界变差存在唯一的充要条件,并利用常数变易法得到其通解公式.本文结果是对线性常微分方程连续解的本质推广.In this paper,by using the generalized ordinary differential equation theory,the relationships between the first-order linear impulsive differential equation and the generalized linear ordinary differential equation are discussed.Necessary and suffcient conditions are given for the existence and uniqueness of bounded variation solutions to the initial value problem of the first-order linear impulsive differential equation,and the general solution formula are obtained by using the method of variation of constants.These results essentially generalize the existing continuous solution to the linear ordinary differential equation.

关 键 词：线性脉冲微分方程 初值问题 有界变差解 常数变易法 

分 类 号：O175.12[理学—数学]