On the uniqueness of the limit cycle for the Liénard equation with \(f(x)\) not sign-definite
type: Item
instance of: scholarly article
title: On the uniqueness of the limit cycle for the Liénard equation with \(f(x)\) not sign-definite
zbMATH Open document ID: 1383.34054
author: Gabriele Villari
author: Fabio Zanolin
published in: Applied Mathematics Letters
publication date: 2017-11-22T00:00:00Z
review text: Consider the Liénard equation \[ \ddot x+ f(x)\dot x+ g(x)=0.\tag{\(*\)} \] The authors prove a theorem guaranteeing that \((*)\) has at most one limit cycle. The feature of their result consists in the fact that the classical assumption of sign-definiteness of \(f(x)\) is relaxed.
reviewed by: Klaus R. Schneider
Mathematics Subject Classification ID: 34C05
zbMATH DE Number: 6811198
zbMATH Keywords: Liénard equation
zbMATH Keywords: limit cycles
zbMATH Keywords: uniqueness
MaRDI profile type: Publication
full work available at URL: j.aml.2017.09.004
OpenAlex ID: W2756238295
cites work: A general equation for relaxation oscillations
cites work: Sopra l'equazione di A. Lienard delle oscillazioni di rilassamento
cites work: On the non-uniqueness of periodic solutions for an asymmetric Liénard equation
cites work: A note on existence and uniqueness of limit cycles for Liénard systems
cites work: Uniqueness of limit cycles for a class of planar vector fields
cites work: Q4376648
cites work: On the improved Massera’s theorem forthe unique existence of the limit cyclefor a Lienard equation
cites work: Q4486929
cites work: Limit cycle uniqueness for a class of planar dynamical systems
cites work: Q3712636
cites work: Q2981046
cites work: On the uniqueness and nonexistence of limit cycles for predator prey systems
cites work: Q3293556
cites work: An extension of Dragilev's theorem for the existence of periodic solutions of the Liénard equation
cites work: Q4913608
cites work: Qualitative analysis of the phase portrait for a class of planar vector fields via the comparison method
cites work: On Massera's theorem concerning the uniqueness of a periodic solution for the Liénard equation. When does such a periodic solution actually exist?
cites work: Q3144730
cites work: Van der Pol and the history of relaxation oscillations: Toward the emergence of a concept
cites work: Q3162560
cites work: Q5580482
DOI: 10.1016/J.AML.2017.09.004
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description: scientific article; zbMATH DE number 6811198