Relativistic equations with singular potentials Arcoya Álvarez, David Sportelli, Caterina Lorentz force equation Relativistic pendulum equation Mountain pass theorem Global continuation theorem Funding for open access publishing: Universidad de Granada/CBUA The first part of this paper concern with the study of the Lorentz force equation [GRAPHICS] in the relevant physical configuration where the electric field (E) over right arrow has a singularity in zero. By using Szulkin's critical point theory, we prove the existence of T-periodic solutions provided that T and the electric and magnetic fields interact properly. In the last part, we employ both a variational and a topological argument to prove that the scalar relativistic pendulum-type equation [GRAPHICS] admits at least a periodic solution when h is an element of L-1(0, T) and G is singular at zero. 2023-07-17T09:55:35Z 2023-07-17T09:55:35Z 2023-04-17 journal article Arcoya, D., Sportelli, C. Relativistic equations with singular potentials. Z. Angew. Math. Phys. 74, 91 (2023). [https://doi.org/10.1007/s00033-023-01977-z] https://hdl.handle.net/10481/83810 10.1007/s00033-023-01977-z eng http://creativecommons.org/licenses/by/4.0/ open access Atribución 4.0 Internacional Springer Nature