The Extendability and Uniqueness of Solutions of Ordinary Differential Equations
In a recent paper  the author obtained results on the extendability of solutions of perturbed differential equations. The question of the extendability of solutions of differential equations is a fundamental and important property since questions of stability and boundedness require extendability. In this paper we continue our study of extendability of perturbed scalar differential equations. Our somewhat surprising results also extend to the question of uniqueness of the zero solution of perturbed equations satisfying an Osgood condition  (See also  for recent results on the uniqueness of perturbed systems.) Examples are provided to demonstrate the strength of our results. The interested reader may look in , ,  for other results on extendability.