Abstract
A Newtonian equation in the plane is considered. There is a central force (attractive or repulsive) and an external force λh(t), periodic in time. The periodic second primitive of h(t) defines a planar curve and the number of periodic solutions of the differential equation is linked to the number of loops of this curve, at least when the parameter λ is large.
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Amster, P., Haddad, J., Ortega, R. et al. Periodic motions in forced problems of Kepler type. Nonlinear Differ. Equ. Appl. 18, 649–657 (2011). https://doi.org/10.1007/s00030-011-0111-8
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DOI: https://doi.org/10.1007/s00030-011-0111-8