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On restricted uniqueness for systems of ordinary differential equations

Authors: J. M. Bownds and J. B. Díaz
Journal: Proc. Amer. Math. Soc. 37 (1973), 100-104
MSC: Primary 34A10
MathSciNet review: 0304739
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Abstract: A uniqueness theorem is proved, for not necessarily Lipschitzian systems of ordinary differential equations, $ y' = f$. This theorem compares with one of Okamura and Murakami, in that, here, at the expense of assuming a certain additional smoothness for f on open sets, no assumption is made regarding the existence of an auxiliary positive definite (Lyapunov) function. An example compares the relative applicability of the two theorems.

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Keywords: Ordinary differential equations, initial-value problems, uniqueness, Lyapunov functions
Article copyright: © Copyright 1973 American Mathematical Society