Estimate of the number of periodic solutions via the twist number
type: Item
instance of: scholarly article
title: Estimate of the number of periodic solutions via the twist number
zbMATH Open document ID: 0881.34063
author: Vieri Benci
author: Donato Fortunato
published in: Journal of Differential Equations
publication date: 1998-02-25T00:00:00Z
review text: The authors consider the dynamical system of the form \[ \ddot x+ V'(x)=0, \] where \(x\in\mathbb{R}^N\), \(V\in C^2(\mathbb{R}^N,\mathbb{R})\) and the gradient \(V'(x)\) is asymptotically linear for \(|x|\to\infty\). It is assumed also that the potential \(V\) has a finite number of non-degenerate critical points \(z_1,\dots,z_n\). Starting from the positive eigenvalues of the Hessian matrices \(V''(z_i)\), the authors define the global twist number of the system and using this characteristic they give a lower estimate for the number \(n(T)\) of non-constant \(T\)-periodic solutions of the system for \(T\) sufficiently large.
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 37-XX
zbMATH DE Number: 1000141
zbMATH Keywords: dynamical system
zbMATH Keywords: global twist number
zbMATH Keywords: \(T\)-periodic solutions
reviewed by: Valerii V. Obukhovskij
MaRDI profile type: Publication
full work available at URL: jdeq.1996.3199
OpenAlex ID: W2082759802
DOI: 10.1006/JDEQ.1996.3199
description: scientific article; zbMATH DE number 1000141