On the existence of forced oscillations for the spherical pendulum acted on by a retarded periodic force

We show that, under mild conditions, T-periodic retarded functional motion equations on even-dimensional spheres admit forced oscillations. In this way we extend analogous results for the undelayed case due to the last two authors. A crucial role in our argument is played by a quite general continuation result, obtained in a recent paper, for forced oscillations of retarded functional motion equations on compact topologically nontrivial boundaryless manifolds.