A Uniqueness Theorem for Ordinary Differential Equations

Abstract

The uniqueness theorem of this paper answers an open question for a system of differential equations arising in a certain n-body problem of classical electrodynamics. The essence of the result can be illustrated using the scalar prototype equation $x' = g_1 (x) + g_2 (t + x)$ with $x(0) = 0$. The solution of the latter will be unique provided $g_1 $ and $g_2 $ are continuous positive functions of bounded variation.