Noncollision periodic solutions to some singular dynamical systems with very weak forces
The investigation for the existence and variational properties of periodic solutions of the equation \(-\ddot x= \nabla F(x)\), with Keplerian type potentials, is studied. The authors prove a double variational characterization of the set of all the periodic solutions of the Kepler problem. A sufficient condition for the existence of a periodic solution with prescribed period of energy for autonomous second- order differential systems (fixed period problem, fixed energy problem) is provided and the proofs are based on linking arguments.
scientific article; zbMATH DE number 759463