On Carathéodory’s conditions for the initial value problem
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- by D. C. Biles and P. A. Binding
- Proc. Amer. Math. Soc. 125 (1997), 1371-1376
- DOI: https://doi.org/10.1090/S0002-9939-97-03942-7
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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.”References
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Bibliographic 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
- 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
- © Copyright 1997 American Mathematical Society
- 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