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On Nagumo's Condition

Published online by Cambridge University Press:  20 November 2018

Thomas Rogers
Thomas Rogers*
Affiliation:
University of Alberta, Edmonton, Alberta
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The classical uniqueness theorem of Nagumo [1] for ordinary differential equations is as follows.

Theorem. If f(t, y) is continuous on 0≤t≤1, -∞<y<∞ and if

then there is at most one solution to the initial value problem y'=f(t, y), y(0)=0.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 15 , Issue 4 , December 1972 , pp. 609 - 611
Copyright
Copyright © Canadian Mathematical Society 1972

References

1. Nagumo, M., Eine hinreichende Bedingung für die Unität der Losung von Differential-gleichungen erster Ordnung, Japan. J. Math. 3 (1926), 107-112.Google Scholar
2. Hille, E., Lectures on ordinary differential equations, Addison-Wesley, Reading, Mass., 1969.Google Scholar