Infinitely many periodic solutions to a Lorentz force equation with singular electromagnetic potential.

We consider the Lorentz force equation d d t (m x ˙ 1 − | x ˙ | 2 / c 2 ) = q (E (t , x) + x ˙ × B (t , x)) , x ∈ R 3 , in the physically relevant case of a singular electric field E. Assuming that E and B are T -periodic in time and satisfy suitable further conditions, we prove the existence of infinitely many T -periodic solutions. The proof is based on a min-max principle of Lusternik-Schnirelmann type, in the framework of non-smooth critical point theory. Applications are given to the problem of the motion of a charged particle under the action of a Liénard-Wiechert potential and to the relativistic forced Kepler problem. [ABSTRACT FROM AUTHOR]