Intersection with the vertical isocline in the Liénard plane
type: Item
instance of: scholarly article
title: Intersection with the vertical isocline in the Liénard plane
zbMATH Open document ID: 1156.34030
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2008-09-10T00:00:00Z
review text: The authors study the problem of whether all trajectories of the Liénard system \[ \dot{x}=y-F(x),\quad \dot{y}=-g(x) \] intersect the vertical isocline \(y=F(x)\). This property is a crucial step for the proof of the existence of oscillatory and periodic solutions and for the global asymptotic stability of the zero solution. As a consequence of the results presented in the paper it is shown that the conjecture given by \textit{T. Hara} and \textit{J. Sugie} in [NoDEA, Nonlinear Differ. Equ. Appl. 2, No.~4, 527--551 (1995; Zbl 0840.34033)] is true.
reviewed by: Jaume Giné
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 34C10
zbMATH DE Number: 5324062
zbMATH Keywords: Liénard system
zbMATH Keywords: periodic solution
zbMATH Keywords: oscillation problem
author: A. Aghajani
author: Amir Moradifam
MaRDI profile type: Publication
full work available at URL: j.na.2007.03.040
OpenAlex ID: W1995597815
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DOI: 10.1016/J.NA.2007.03.040
description: scientific article; zbMATH DE number 5324062