Note on periodic solutions of relativistic pendulum type systems

Abstract

We establish multiplicity results of periodic solutions for relativistic pendulum type systems of ordinary differential equations. We provide a different approach to the problems and answer some questions raised in [Periodic solutions of the forced relavitistic pendulum, Differential Integral Equations 23 (2010), 801-810], [Periodic solutions of Lagrangian systems of relatvitistic oscillations, Comm. Appl. Anal. 15 (2011), 235-250] by Brezis and Mawhin recently.