Periodic solutions with prescribed energy for some Keplerian \(N\)-body problems
type: Item
instance of: scholarly article
title: Periodic solutions with prescribed energy for some Keplerian \(N\)-body problems
zbMATH Open document ID: 0855.70006
DOI: 10.1016/S0294-1449(16)30170-6
author: Kazunaga Tanaka
author: Enzo Vitillaro
author: A. Ambrosetti
published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire
publication date: 1995-12-18T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/78345
review text: The existence of periodic solutions with prescribed energy \(h\) of the system \(\ddot x+ v'(x)= 0\), \({1\over 2} |\dot x|^2+ v(x)= h\) with \(x= (x_1, x_2,\dots, x_N)\), \(x_j\in \mathbb{R}^k\), \(v(x)= {1\over 2} \sum_{i\neq j} v_{ij}(x_i- x_j)\), \(v_{ij}(\xi)= - |\xi|^{-a}\), \(a> 0\), is proved for a class of Keplerian-like \(N\)-body problem, employing critical point theory with boundary conditions.
Mathematics Subject Classification ID: 70F10
Mathematics Subject Classification ID: 58E05
Mathematics Subject Classification ID: 37J99
zbMATH DE Number: 827027
zbMATH Keywords: existence
zbMATH Keywords: boundary conditions
reviewed by: Maria Gousidou-Koutita
MaRDI profile type: Publication
cites work: Closed orbits of fixed energy for singular Hamiltonian systems
cites work: Addendum to: Closed orbits of fixed energy for a class of N-body problems
cites work: Periodic solutions of singular Lagrangian systems
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cites work: A prescribed energy problem for a singular Hamiltonian system with a weak force
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description: scientific article; zbMATH DE number 827027