Periodic solutions of some autonomous Liénard equations with relativistic acceleration
type: Item
instance of: scholarly article
title: Periodic solutions of some autonomous Liénard equations with relativistic acceleration
zbMATH Open document ID: 1384.34039
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2017-08-03T00:00:00Z
review text: Consider the relativistic Liénard equation \[ {d\over dt} {\dot x\over \sqrt{1-\dot x^2}}+ f(x)\dot x+ g(x)= 0.\tag{\(*\)} \] The authors derive conditions on the functions \(f\) and \(g\) such that \((*)\) has at least one stable limit cycle. The proof is based on the application of the Poincaré-Bendixson theorem. The approach and the existence conditions are distinct from those recently obtained by \textit{S. Pérez-González} et al. [J. Math. Anal. Appl. 439, No. 2, 745--765 (2016; Zbl 1346.34027)].
Mathematics Subject Classification ID: 34C05
zbMATH DE Number: 6756449
zbMATH Keywords: periodic orbits
zbMATH Keywords: limit cycles
zbMATH Keywords: Van der Pol relativistic equation
zbMATH Keywords: Liénard relativistic equation
author: Jean Mawhin
author: Gabriele Villari
reviewed by: Klaus R. Schneider
MaRDI profile type: Publication
full work available at URL: j.na.2017.05.001
OpenAlex ID: W2617213512
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DOI: 10.1016/J.NA.2017.05.001
description: scientific article; zbMATH DE number 6756449