The Existence and Uniqueness of Solutions to N-Body Problem of Electrodynamics

Given $n$ charges interacting with each other according to Feynman's law. Let $(r_j(t),v_j(t))$ denote the position and velocity of the charge $q_j.$ The list $y(t)$ of all such vectors is called a trajectory. A Lipschitzian trajectory $x(t), (t\le0),$ with continuous derivative, on which the velocities do not exceed some limiting velocity $v