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

Alberto Boscaggin, Walter Dambrosio, Duccio Papini

We consider the Lorentz force equation $$ \frac{d}{dt}\left(\frac{m\dot{x}}{\sqrt{1-|\dot{x}|^{2}/c^{2}}}\right) = q \left(E(t,x) + \dot x \times B(t,x)\right), \qquad x \in \mathb…