Existence and stability of periodic solutions for relativistic singular equations
type: Item
instance of: scholarly article
title: Existence and stability of periodic solutions for relativistic singular equations
zbMATH Open document ID: 1366.34058
author: Jifeng Chu
author: Zaitao Liang
author: Shiping Lu
author: Fang-Fang Liao
published in: Communications on Pure and Applied Analysis
publication date: 2017-02-03T00:00:00Z
review text: The authors provide sufficient conditions for the existence and stability of periodic solutions of the equation \[ \left(\frac{x'}{\sqrt{1-(x')^2}}\right)'+ cx' + f(x) = e(t). \] This is a particular case of a scalar \(\phi\)-Laplacian equation, where the first term is the relativistic acceleration. The authors are interested in the case when the nonlinearity \(f(x)\) exhibits some type of singularity, i.e., it becomes unbounded at a given point. The existence result is based on the continuation method of coincidence degree theory, whereas the stability relies on a known relation between Brouwer degree and stability of periodic solutions due to \textit{R. Ortega} [Boll. Unione Mat. Ital., VII. Ser., B 3, No. 3, 533--546 (1989; Zbl 0686.34052)].
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 34D20
Mathematics Subject Classification ID: 47N20
zbMATH DE Number: 6680520
zbMATH Keywords: relativistic singular equations
zbMATH Keywords: stability
zbMATH Keywords: positive periodic solutions
MaRDI profile type: Publication
full work available at URL: cpaa.2017029
OpenAlex ID: W2574872756
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DOI: 10.3934/CPAA.2017029
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description: scientific article; zbMATH DE number 6680520