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

MA Xue-min, LI Bao-lin, LIN Chang-wei

doi:10.13371/j.cnki.chin.q.j.m.2015.04.014

Chinese Quarterly Journal of Mathematics >

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

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

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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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

Cite this article

MA Xue-min, LI Bao-lin, LIN Chang-wei . Continuous Dependence of Bounded Φ-variation Solutions on Parameter for a Class of Discontinuous Systems[J]. Chinese Quarterly Journal of Mathematics, 2015 , 30(4) : 610 -619 . DOI: 10.13371/j.cnki.chin.q.j.m.2015.04.014

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