Regularized variational principles for the perturbed Kepler problem

The goal of the paper is to develop a method that will combine use variational techniques with regularization methods in order study existence and multiplicity results for periodic Dirichlet problem associated perturbed Kepler systemx¨=−x|x|3+p(t),x∈Rd, where d≥1, p:R→Rd smooth T-periodic, T>0. critical points action functional proved via non-local change variables inspired by Levi-Civita Kustaanheimo-Stiefel techniques. As an application we prove has infinitely many generalized T-periodic solutions d=2 d=3, without any symmetry assumptions on p.