Chinese Quarterly Journal of Mathematics ›› 2015, Vol. 30 ›› Issue (4): 610-619.doi: 10.13371/j.cnki.chin.q.j.m.2015.04.014

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

  

  1. 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
  • Received:2014-03-28 Online:2015-12-30 Published:2020-11-19
  • About author: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.
  • 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);

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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