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Description

The equations of motion of Wheeler-Feynman electrodynamics are given by a set of functional differential equations involving state-dependent delayed and advanced arguments. In the case of two particles of equal charge and when the motion is restricted to a straight line G. Bauer proved existence of solutions which are characterized by their asymptotic properties. In a joint work with G. Bauer and D. Dürr we reformulated the problem of existence of solutions for Wheeler-Feynman electrodynamics so that it can be studied via an initial value problem. For given Newtonian Cauchy data we prove existence of trajectories which fulfill the Wheeler-Feynman equations on a finite time interval for N extended particles with any charge and without a geometrical restriction on the motion in three dimensions. We discuss conditions under which the applied method would yield Wheeler-Feynman solutions for all times.