Bounds for the periods of periodic solutions of ordinary differential equations
type: Item
instance of: scholarly article
title: Bounds for the periods of periodic solutions of ordinary differential equations
zbMATH Open document ID: 1388.34036
author: A. O. Ignat'ev
published in: Ukrainian Mathematical Journal
publication date: 2018-02-23T00:00:00Z
review text: Consider in \(\mathbb{R}^n\) the nonautonomous differential system \[ {dx\over dt}= X(t,x)\tag{\(*\)} \] under the assumption that \(X\) is continuously differentiable and that has a periodic solution with period \(T>0\) in some region \(\Omega\subset \mathbb{R}^n\). Additionally, the author supposes that there exists \[ \lambda:=\sup_{\substack{ t\in\mathbb{R}_+\\ x\in\Omega}}\;{\|{d\over dt}\,X(t, x(t))|_{(*)}\|\over \| X(t,x)\|}. \] Then he proves \(T\geq {2\pi\over\lambda}\).
reviewed by: Klaus R. Schneider
Mathematics Subject Classification ID: 34C25
zbMATH DE Number: 6842821
MaRDI profile type: Publication
full work available at URL: s11253-016-1188-3
OpenAlex ID: W2405839141
cites work: Periods of Periodic Solutions and the Lipschitz Constant
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cites work: Q5795778
DOI: 10.1007/S11253-016-1188-3
description: scientific article; zbMATH DE number 6842821