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We consider a Kepler problem in dimension two or three, with a time-dependent$T$-periodic perturbation. We prove that for any prescribed positive integer$N$, there exist at least $N$ periodic solutions (with period $T$) as long asthe perturbation is small enough. Here the solutions are understood in ageneral sense as they can have collisions. The concept of generalized solutionsis defined intrinsically and it coincides with the notion obtained in CelestialMechanics via the theory of regularization of collisions.

Periodic solutions and regularization of a Kepler problem with time-dependent perturbation