On restricted uniqueness for systems of ordinary differential equations

Abstract

A uniqueness theorem is proved, for not necessarily Lipschitzian systems of ordinary differential equations, y ′ = f 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.