Periodic linear motions with multiple collisions in a forced Kepler type problem
In this paper the authors extend the proof of the existence of multiple periodic linear motions with collisions for a periodically forced Kepler problem, presented by R. Ortega [Port. Math. (N.S.) 68, No. 2, 149--176 (2011; Zbl 1235.34136)] , in the equation $\ddot{u} =-1/u^2+p(t)\), \(u>0\), to a forced Kepler type problem \(\ddot{u} =-1/u^\alpha+p(t)\), \(u>0\), \(\alpha=2\) or \(\alpha\ge 4\). They generalize the results of Ortega for the existence of positive periodic solutions with \(n\) collisions in the interval \([0,2M\pi]\), for each \(M\) and \(n\). For this proof, the authors apply the Poincaré-Birkhoff theorem. The paper ends with no conclusions but there is an Appendix, where the authors present some auxiliary proofs.
scientific article; zbMATH DE number 6919404