Pablo Amster, Maria Cristina Mariani
Periodic solutions of the forced pendulum equation with friction
(16K, TeX)
ABSTRACT. This paper is devoted
to the study of the general forced pendulum equation in the
presence of friction,
$$u'' + a(t)u' + b(t) \sin u = f(t)$$
with $a,b\in C([0,T])$ and
$f\in L^2(0,T)$.
We'll show that $T$-periodic solutions may be obtained as zeroes of a
$2\pi$-periodic
continuous real function. Furthermore, the existence of infinitely many solution
s is
proved under appropiate conditions on $a,b$ and $f$.