Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On Carathéodory's conditions
for the initial value problem


Authors: D. C. Biles and P. A. Binding
Journal: Proc. Amer. Math. Soc. 125 (1997), 1371-1376
MSC (1991): Primary 34A12; Secondary 34A40
MathSciNet review: 1403114
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We prove a local existence theorem of Carathéodory-Goodman type for $\dot {x}(t)=f(t,x(t))$ where instead of $f(t,\alpha )$ being continuous in $\alpha $ we require only that it have no ``downward discontinuities.''


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 34A12, 34A40

Retrieve articles in all journals with MSC (1991): 34A12, 34A40


Additional Information

D. C. Biles
Affiliation: Department of Mathematics, Western Kentucky University, Bowling Green, Kentucky 42101
Email: Daniel.Biles@wku.edu

P. A. Binding
Affiliation: Department of Mathematics and Statistics, University of Calgary, Alberta, Canada T2N 1N4
Email: binding@acs.ucalgary.ca

DOI: http://dx.doi.org/10.1090/S0002-9939-97-03942-7
PII: S 0002-9939(97)03942-7
Received by editor(s): November 8, 1995
Additional Notes: The second author’s research was supported by NSERC of Canada and the I. W. Killam Foundation.
Communicated by: Hal L. Smith
Article copyright: © Copyright 1997 American Mathematical Society