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

DOI:
https://doi.org/10.1090/S0002-9939-97-03942-7

MathSciNet review:
1403114

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Abstract | References | Similar Articles | Additional Information

Abstract: We prove a local existence theorem of Carathéodory-Goodman type for where instead of being continuous in we require only that it have no ``downward discontinuities.''

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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:
https://doi.org/10.1090/S0002-9939-97-03942-7

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