Cristian Bereanu
University of Bucharest, Bucharest, Romania

In this talk we consider the Lorentz force equation with periodic conditions on a fixed interval. In Special Relativity, this equation models the motion of a slowly accelerated electron under the influence of an electric field and a magnetic field. We provide a rigourous critical point theory by showing that the solutions are the critical points in the Szulkin’s sense of the corresponding Poincare non-smooth Lagrangian action. By using a novel minimax principle, we prove a variety of existence and multiplicity results. This is a joint work with D. Arcoya and P. Torres.