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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A uniqueness theorem for $ y'=f(x,y),\;y(x\sb 0)=y\sb 0$


Author: Armando Majorana
Journal: Proc. Amer. Math. Soc. 111 (1991), 215-220
MSC: Primary 34A12
MathSciNet review: 1028290
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Abstract: Consider the initial value problem for a first-order differential equation

$\displaystyle y' = f(x,y),\quad y({x_0}) = {y_0}.$

In this paper a new uniqueness criterion is proved. This criterion is related to the numeric equation

$\displaystyle u = {y_0} + (t - {x_0})f(t,u).$

It is also shown that some well-known uniqueness theorems are consequences of our result.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1991-1028290-X
PII: S 0002-9939(1991)1028290-X
Keywords: Ordinary differential equations, initial value problem, uniqueness
Article copyright: © Copyright 1991 American Mathematical Society