Periodic solutions for Liénard equation with an indefinite singularity
type: Item
instance of: scholarly article
title: Periodic solutions for Liénard equation with an indefinite singularity
zbMATH Open document ID: 1411.34058
author: Yuanzhi Guo
author: Shiping Lu
author: Lijuan Chen
published in: Nonlinear Analysis. Real World Applications
publication date: 2019-02-27T00:00:00Z
review text: The authors study the existence of positive periodic solutions for a scalar equation of the type \[ x''(t)+f(x(t))x'(t)+\varphi(t)x^m(t)-\frac{\alpha(t)}{x^\mu(t)}=0. \] Here, the function \(f\) may have a singularity at the origin, and the signs of the \(T\)-periodic functions \(\varphi(t)\) and \(\alpha(t)\) are allowed to change. They prove some existence results by the use of continuation theory, under some technical assumptions, thus partly solving a problem raised by Hakl, Torres and Zamora.
reviewed by: Alessandro Fonda
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 47N20
zbMATH DE Number: 7030118
zbMATH Keywords: Liénard equation
zbMATH Keywords: continuation theorem
zbMATH Keywords: periodic solution
zbMATH Keywords: singularity
MaRDI profile type: Publication
full work available at URL: j.nonrwa.2018.07.024
OpenAlex ID: W2887594930
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DOI: 10.1016/J.NONRWA.2018.07.024
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description: scientific article; zbMATH DE number 7030118