Noncollision periodic solutions to some singular dynamical systems with very weak forces
type: Item
instance of: scholarly article
title: Noncollision periodic solutions to some singular dynamical systems with very weak forces
zbMATH Open document ID: 0826.34039
author: Miguel Ramos
author: Susanna Terracini
published in: Journal of Differential Equations
publication date: 1995-05-30T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 70K25
Mathematics Subject Classification ID: 70F10
Mathematics Subject Classification ID: 70F15
zbMATH DE Number: 759463
zbMATH Keywords: periodic solutions
zbMATH Keywords: Keplerian type potentials
zbMATH Keywords: variational characterization
zbMATH Keywords: Kepler problem
reviewed by: Maria Gousidou-Koutita
MaRDI profile type: Publication
full work available at URL: jdeq.1995.1069
OpenAlex ID: W2048063980
DOI: 10.1006/JDEQ.1995.1069
description: scientific article; zbMATH DE number 759463