Discontinuous Systems and the Henstock-Kurzweil Integral

Journal of Mathematical Analysis and Applications

Volumn 229, Issue 1, 1999, Pages 119-136

  Congxin, Wu ^b   Baolin, Li ^b   Lee, E Stanley ^a  

^a Sunflower Networking Group   (United States)

^b NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0042044433     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmaa.1998.6149     Document Type: Article

References (15)

1. He J., Chen P. Some aspects of the theory and applications of discontinuous differential equations. Adv. in Math. 16:1987;17-32.
2. Filippov A. F. Differential equations with discontinuous right-hand side. Math. USSR-Sb. 51:1960.
3. Hajek O. Discontinuous differential equation I, II. J. Differential Equations. 32:1979;149-185.
4. Kurzweil J. Generalized ordinary differential equations and continuous dependence on a parameter. Czechoslovak Math. J. 7:1957;418-446.
5. Henstock R. Definitions of Riemann type of the variational integrals. Proc. London Math. Soc. 11:1961;402-418.
6. Henstock R. Lectures on the Theory of Integration. 1988;World Scientific, Singapore.
7. Lee P. Y., Chew T. S. A better convergence theorem for Henstock integrals. Bull. London Math. Soc. 17:1985;557-574.
8. Lee P. Y. Lanzhou Lectures on Henstock Integration. 1989;World Scientific, Singapore.
9. Pfeffer W. F. Integration by parts for the generalized Riemann-Stieltjes integral. J. Austral. Math. Soc. Ser. A. 34:1983;229-231.
10. Ostaszewski K., Sochacki J. Gronwall's inequality and the Henstock integral. J. Math. Anal. Appl. 127:1987;370-374.
11. Li B. The topological structure on the space of (H) integrable functions. J. Math. 14:1994;61-68.
12. Caratheodory C. Vorlesungen über Relle Funktionen. 1918;Teubner, Leipzig.
13. Coddington E. A., Levinson N. Theory of Ordinary Differential Equations. 1955;McGraw-Hill, New York.
14. Saks S. Theory of the Integral. 1964;Dover, New York.
15. ap = fxy. J. Math. Anal. Appl. 127:1987;365-376.