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Proceedings of the American Mathematical Society

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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
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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.''

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Additional Information

D. C. Biles
Affiliation: Department of Mathematics, Western Kentucky University, Bowling Green, Kentucky 42101

P. A. Binding
Affiliation: Department of Mathematics and Statistics, University of Calgary, Alberta, Canada T2N 1N4

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