Ambrosetti, A.; Bessi, U. Multiple periodic trajectories in a relativistic gravitational field. (English) Zbl 0725.34038 Variational methods, Proc. Conf., Paris/Fr. 1988, Prog. Nonlinear Differ. Equ. Appl. 4, 373-381 (1990). [For the entire collection see Zbl 0713.00009.] The paper deals with a class of conservative systems with singular potentials. The existence of n closed, geometrically distinct trajectories with prescribed energy is proved. The result applies, for example, to potentials arising in the Post-Newtonian Celestial Mechanics, when the Kepler potential \(-| x|^{-1}\) is substituted by \(- | x|^{-1}-k| x|^{-2}\) where \(k\approx 1/c^ 2\), c \(=\) speed of light. The paper is related to other ones dealing with conservative systems with singular potentials: see, for example, the first author and V. Coti Zelati [Arch. Ration. Mech. Anal. 112, No.4, 339-362 (1990)] and references therein. Reviewer: A.Ambrosetti Cited in 3 Documents MSC: 34C25 Periodic solutions to ordinary differential equations 83C40 Gravitational energy and conservation laws; groups of motions 70F15 Celestial mechanics Keywords:periodic solutions; conservative systems with singular potentials; Celestial Mechanics; Kepler potential Citations:Zbl 0713.00009 PDFBibTeX XML