Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

On Carathéodory's conditions for the initial value problem

Author(s): D. C. Biles; 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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