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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.

References [Enhancements On Off] (What's this?)

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Keywords: Ordinary differential equations, initial value problem, uniqueness
Article copyright: © Copyright 1991 American Mathematical Society