Solvability of the forced relativistic pendulum with a derivative-dependent coefficient

We deal with the solvability of the forced pendulum in the relativistic regime. As a novelty with respect to most references in the mathematical literature, and based on an alternative framework discussed in some physical papers, we take into account also the relativistic effects in the forces acting on the pendulum which lead to the study of a [Formula: see text]-laplacian equation with an unbounded derivative-dependent term. In this new relativistic setting we recover several results about the structure of the solvability set that are well–known for the classical pendulum. We also show that the solvability set for the classical pendulum is the limit of the relativistic one when the speed of light blows up to infinity.