We provide a method for the count and the variational characterization of periodic solutions to forced pendulum-type equation. This is achieved by reducing the problem to the study of a real function of one variable. This paper generalizes some results obtained by G. Tarantello.
"On the count and the classification of periodic solutions to forced pendulum-type equations." Differential Integral Equations 11 (3) 503 - 520, 1998. https://doi.org/10.57262/die/1367341065