Programa de Pós-Graduação em Matemática

Relativistic pendulum equation

Prof. David Arcoya
Universidad de Granada

Date: 14th February 11:00 am - 11:45 am (UTC -3) Link: PPGM/UFSCar Youtube channel

Abstract: We survey the results of the joint paper with Antonio Ambrosetti (Differential and
Integral equations, 33 (2020), 92-112). We consider the equation


modeling, if F'(u) = sin u, the motion of the free relativistic planar pendulum. Using the
critical point theory for non-smooth functionals due to Szulkin, we prove the existence of
non-trivial T periodic solutions provided T is sufficiently large.
We also show the existence of periodic solutions to the free and forced relativistic spherical
pendulum, where F' is substituted by F'(u)−h2G'(u) ∼ sin u−h2cos u/sin3 u, h ∈ R.