The minimal period problem for nonconvex even second order Hamiltonian systems
type: Item
instance of: scholarly article
title: The minimal period problem for nonconvex even second order Hamiltonian systems
zbMATH Open document ID: 0898.34042
author: Guihua Fei
author: Tixiang Wang
published in: Journal of Mathematical Analysis and Applications
publication date: 1998-10-15T00:00:00Z
review text: The authors consider classical Hamiltonian systems \[ \ddot x + V'(x)=0 , \qquad \forall\;x\in \mathbb{R}^N \] with \(V\in C^2({\mathbb{R}}^N,{\mathbb{R}})\) and \[ V(x)={1\over 2} h_0x\cdot x+\widetilde VB(x) , \qquad \forall\;x\in{\mathbb{R}}^N , \] with \(h_0\in {{\mathcal L}}_s({\mathbb{R}}^N)\), \(x\cdot x\) is the inner product, \(\widetilde V\) is even, \(\widetilde V(-x)=\widetilde V(x)\), \(\forall\;x\in{\mathbb{R}}^N\) and \(\widetilde V(x)=o(| x| ^2) \) as \(| x| \to 0\). By using variational methods, they obtain estimates for the minimal period of the corresponding nonconstant periodic solutions to superquadratic and asymptotically linear Hamiltonian systems.
reviewed by: G.V.Khmelevskaja-Plotnikova
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 37J99
zbMATH DE Number: 1115432
zbMATH Keywords: nonconvex even second-order Hamiltonian systems
zbMATH Keywords: minimal period problem
zbMATH Keywords: super-quadratic
zbMATH Keywords: asymptotically linear
zbMATH Keywords: symmetric Morse index
MaRDI profile type: Publication
full work available at URL: jmaa.1997.5666
OpenAlex ID: W1973559381
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DOI: 10.1006/JMAA.1997.5666
description: scientific article; zbMATH DE number 1115432