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.
@article{arxiv.1105.2156,
title = {On the Nagumo uniqueness theorem},
author = {Octavian G. Mustafa and Donal O'Regan},
journal= {arXiv preprint arXiv:1105.2156},
year = {2011}
}