Periodic solutions of singular radially symmetric systems with superlinear growth

We prove the existence of infinitely many periodic solutions for periodically forced radially symmetric systems of second-order ODE's, with a singularity of repulsive type, where the nonlinearity has a superlinear growth at infinity. These solutions have periods, which are large integer multiples of the period of the forcing, and rotate exactly once around the origin in their period time, while having a fast oscillating radial component. Analogous results hold in the case of an annular potential well.