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一阶线性脉冲微分方程初值问题的有界变差解
  • ISSN号：1005-3085
  • 期刊名称：《工程数学学报》
  • 时间：0
  • 分类：O175.12[理学—数学;理学—基础数学]
  • 作者机构：[1]西北师范大学数学与信息科学学院,兰州730070
  • 相关基金：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）
作者： 李宝麟[1], 李林强[1]
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, linear impulsive differential equations, initial value problems, bounded variation solution, the method of variation of constants
中文摘要：

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.

英文摘要：

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.

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期刊信息
  • 《工程数学学报》
  • 北大核心期刊（2011版）
  • 主管单位:教育部
  • 主办单位:西安交通大学
  • 主编：李大潜
  • 地址：西宁市咸宁西路28号西安交通大学数学与统计学院
  • 邮编：710049
  • 邮箱：jgsx@mail.xjtu.edu.cn
  • 电话：029-82667877
  • 国际标准刊号：ISSN：1005-3085
  • 国内统一刊号：ISSN：61-1269/O1
  • 邮发代号:
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  • 被引量:6741