Bessi, U. Multiple closed orbits of fixed energy for gravitational potentials. (English) Zbl 0787.34029 J. Differ. Equations 104, No. 1, 1-10 (1993). The paper gives for any fixed \(h<0\) a lower bound for the number of geometrically distinct closed noncollision trajectories of minimal period of the problem \(\ddot q+V'(q)=0\), \({1\over 2} | \dot q |^ 2+V(q)=h\). Here \(V\) is a potential which behaves like \(V(x)\cong-1/ | x |^ \gamma\) where \(1\leq \gamma<2\). In the proof of the main theorem variational methods are applied. This work is an extension of Ambrosetti’s and the author’s investigations to the case of gravitational potentials. Reviewer: Á.Bosznay (Budapest) Cited in 8 Documents MSC: 34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations 70F99 Dynamics of a system of particles, including celestial mechanics Keywords:lower bound for the number of geometrically distinct closed noncollision trajectories of minimal period; variational methods; gravitational potentials PDFBibTeX XMLCite \textit{U. Bessi}, J. Differ. Equations 104, No. 1, 1--10 (1993; Zbl 0787.34029) Full Text: DOI