Existence of at least two periodic solutions of the forced relativistic pendulum

Abstract

Using Szulkin's critical point theory, we prove that the relativistic forced pendulum with periodic boundary value conditions, has at least two solutions not differing by a multiple of 2π for any continuous function h: [0, T] → ℝ with ∫ T 0 h(t)dt = 0 and any μ ≠0. The existence of at least one solution has been recently proved by Brezis and Mawhin. © 2011 American Mathematical Society.