On the existence of periodic oscillations for pendulum-type equations

We provide new sufficient conditions for the existence of T-periodic solutions for the ϕ-laplacian pendulum equation (ϕ(x′))′ + k x′ + a sin x = e(t), where e ∈ C͠T. Our main tool is a continuation theorem due to Capietto, Mawhin and Zanolin and we improve or complement previous results in the literature obtained in the framework of the classical, the relativistic and the curvature pendulum equations.