An extension of Dragilev's theorem for the existence of periodic solutions of the Liénard equation
type: Item
instance of: scholarly article
title: An extension of Dragilev's theorem for the existence of periodic solutions of the Liénard equation
zbMATH Open document ID: 1328.34026
author: Martina Cioni
author: Gabriele Villari
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2015-09-30T00:00:00Z
full work available at URL: http://hdl.handle.net/2158/903932
review text: Subject of this paper is the well-known and intensively studied Liénard equation. The authors discuss the conditions and methods for guaranteeing the existence of at least one (nontrivial) periodic orbit (referring partly to former papers by one of the present authors). Since the classical Poincaré-Bendixson theorem seems to be the only available device to do this, it is important to construct a so-called winding trajectory by applying either of two methods: the energy method and the method of intersection with the vertical isocline. In this way, the authors derive an improvement of a theorem by \textit{A. V. Dragilev} [Prikl. Mat. Mekh. 16, 85--88 (1952; Zbl 0046.09703)] on the existence of a limit cycle. Finally, they indicate how the conditions may be adjusted in such a way that there exist at least two limit cycles.
reviewed by: Josef Hainzl
Mathematics Subject Classification ID: 34C05
Mathematics Subject Classification ID: 34A34
zbMATH DE Number: 6487753
zbMATH Keywords: Lienard equation
zbMATH Keywords: limit cycle
zbMATH Keywords: Dragilev theorem
zbMATH Keywords: winding trajectory
MaRDI profile type: Publication
OpenAlex ID: W884073476
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DOI: 10.1016/J.NA.2015.06.026
description: scientific article; zbMATH DE number 6487753