数学季刊 >

2015 , Vol. 30 >Issue 4: 610 - 619

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2015.04.014

一类不连续系统Φ-有界变差解对参数的连续依赖性

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  • 1. Department of Mathematics, Dingxi Advanced Teacher's College2. College of Mathermatics and Statistics, Northwest Normal University3. Department of Geography, Dingxi Advanced Teacher's College
MA Xue-min(1981-), female, native of Longxi, Gansu, a lecturer of Dingxi Advanced Teacher's College, M.S.D., engages in generalized ordinary di®erential equation; LI Bao-lin(1963-), male, native of Tianshui, Gansu, a professor of Northwest Normal University, Ph.D., engages in generalized ordinary differential equation; LIN Chang-wei(1983-), female, native of Zhuanghe, Liaoning, a lecturer of Dingxi Advanced Teacher's College, M.S.D., engages in remote sensing and landscape ecology.

收稿日期: 2014-03-28

  网络出版日期: 2020-11-19

基金资助

Supported by the National Natural Science Foundation of China(10771171)； Supported by the 555 Innovation Talent Project of Gansu Province（GS-555-CXRC）； Supported by the Technique Innovation Project of Northwest Normal University（NWNU-KJCXGC-212）； Supported by the Youth Foundation of Dingxi Advanced Teachers College(1333)；

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Continuous Dependence of Bounded Φ-variation Solutions on Parameter for a Class of Discontinuous Systems

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  • 1. Department of Mathematics, Dingxi Advanced Teacher's College2. College of Mathermatics and Statistics, Northwest Normal University3. Department of Geography, Dingxi Advanced Teacher's College
MA Xue-min(1981-), female, native of Longxi, Gansu, a lecturer of Dingxi Advanced Teacher's College, M.S.D., engages in generalized ordinary di®erential equation; LI Bao-lin(1963-), male, native of Tianshui, Gansu, a professor of Northwest Normal University, Ph.D., engages in generalized ordinary differential equation; LIN Chang-wei(1983-), female, native of Zhuanghe, Liaoning, a lecturer of Dingxi Advanced Teacher's College, M.S.D., engages in remote sensing and landscape ecology.

Received date: 2014-03-28

  Online published: 2020-11-19

Supported by

Supported by the National Natural Science Foundation of China(10771171)； Supported by the 555 Innovation Talent Project of Gansu Province（GS-555-CXRC）； Supported by the Technique Innovation Project of Northwest Normal University（NWNU-KJCXGC-212）； Supported by the Youth Foundation of Dingxi Advanced Teachers College(1333)；

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摘要

The functions of bounded Φ-variation are development and generalization of bounded variation functions in the usual sense.Henstock-Kurzweil integral is a very useful tool for some discontinuous systems. In this paper, by using Henstock-Kurzweil integral, we establish theorems of continuous dependence of bounded Φ-variation solutions on parameter for a class of discontinuous systems on the base of Φ-function. These results are essential generalizations of continuous dependence of bounded variation solutions on parameter for the systems. 

关键词： discontinuous systems; Henstock-Kurzweil integral; bounded Φ-variation solution; continuous dependence

本文引用格式

马学敏, 李宝麟, 林长伟 . 一类不连续系统Φ-有界变差解对参数的连续依赖性[J]. 数学季刊, 2015 , 30(4) : 610 -619 . DOI: 10.13371/j.cnki.chin.q.j.m.2015.04.014

Abstract

The functions of bounded Φ-variation are development and generalization of bounded variation functions in the usual sense.Henstock-Kurzweil integral is a very useful tool for some discontinuous systems. In this paper, by using Henstock-Kurzweil integral, we establish theorems of continuous dependence of bounded Φ-variation solutions on parameter for a class of discontinuous systems on the base of Φ-function. These results are essential generalizations of continuous dependence of bounded variation solutions on parameter for the systems. 

Key words： discontinuous systems; Henstock-Kurzweil integral; bounded Φ-variation solution; continuous dependence

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