On the Nagumo uniqueness theorem
Octavian G. Mustafa, Donal O'Regan

TL;DR
This paper improves the Nagumo uniqueness theorem by establishing a more flexible criterion for the uniqueness of solutions to nonlinear ODEs without Lipschitz conditions, using a reparametrisation of integral curves.
Contribution
It introduces a new approach through reparametrisation to extend the Nagumo theorem to broader classes of nonlinear ODEs without Lipschitz-like nonlinearities.
Findings
Established a more general uniqueness criterion for nonlinear ODEs.
Extended the applicability of Nagumo's theorem beyond Lipschitz conditions.
Provided a simplified proof technique via reparametrisation.
Abstract
By a convenient reparametrisation of the integral curves of a nonlinear ordinary differential equation (ODE), we are able to improve the conclusions of the recent contribution [A. Constantin, Proc. Japan Acad. {\bf 86(A)} (2010), 41--44]. In this way, we establish a flexible uniqueness criterion for ODEs without Lipschitz-like nonlinearities.
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