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

Using Szulkin's critical point theory, we prove that the relativistic forced pendulum with periodic boundary value conditions

$\left (\frac {u'}{\sqrt {1-u'^2}}\right )' +\mu \sin u=h(t), \quad u(0)-u(T)=0=u'(0)-u'(T),$

has at least two solutions not differing by a multiple of $2\pi$ for any continuous function $h:[0,T]\to \mathbb{R}$ with $\int _0^Th(t)dt=0$ and any $\mu \neq 0.$ The existence of at least one solution has been recently proved by Brezis and Mawhin.