Periodic solutions for a class of Lorenz-Lagrangian systems
type: Item
instance of: scholarly article
title: Periodic solutions for a class of Lorenz-Lagrangian systems
zbMATH Open document ID: 0657.34042
DOI: 10.1016/S0294-1449(16)30344-4
published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire
publication date: 1988-01-01T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/78151
review text: The author studies a class of Lorentz-Lagrange systems of the form (*) \(- A\ddot q=\nabla V(q)\) where \(q\in R^ n\), A is a real symmetric matrix with eigenvalues \(\lambda_ i\) \((\lambda_ 1<0)\) and corresponding eigenvectors \(e_ i\) \((1\leq i\leq n)\). By improving some ideas developed in previous papers [\textit{H. Hofer} and \textit{J. Toland}, Math. Ann. 268, 387-403 (1984; Zbl 0569.70017); \textit{J. Toland} [Nonlinear Functional Analysis and its Applications, Proc. NATO Adv. Study Inst. Maratea/Italy 1985, NATO ASI Ser., Ser. C 173, 147-160 (1986; Zbl 0606.58023)] and introducing a new idea, the existence of a periodic solution of the system (*) is proved under hypotheses which involve only the set where \(V>0\).
Mathematics Subject Classification ID: 34C25
zbMATH DE Number: 4073480
zbMATH Keywords: Hamiltonian systems
zbMATH Keywords: Lorentz-Lagrange systems
zbMATH Keywords: real symmetric matrix
author: John F. Toland
reviewed by: Augusto Muracchini
MaRDI profile type: Publication
cites work: Homoclinic, heteroclinic, and periodic orbits for a class of indefinite Hamiltonian systems
cites work: Calculus of variations in the large and classical mechanics
cites work: Q3744931
OpenAlex ID: W33048922
description: scientific article; zbMATH DE number 4073480