A topological approach to the repulsive central motion problem

We look for periodic solutions to nonlinear second order system of equations motivated by the Central Motion Problem. We study the repulsive case, the Coulomb problem of a charge being repelled by a source. Using topological degree methods, we prove that either the problem has a classical solution, or else there exists a family of solutions of perturbed problems that converges uniformly and weakly in H to some limit function u. Furthermore, under appropriate conditions we prove that u is a classical solution. We generalize this results for nonlinearities with a repulsive type singularity.