Periodic solutions for indefinite singular equations with singularities in the spatial variable and non-monotone nonlinearity
type: Item
instance of: scholarly article
title: Periodic solutions for indefinite singular equations with singularities in the spatial variable and non-monotone nonlinearity
zbMATH Open document ID: 1398.34058
author: Manuel Zamora
author: Pablo Amster
published in: Discrete and Continuous Dynamical Systems
publication date: 2018-08-22T00:00:00Z
review text: The author's aim is to prove the existence of a periodic solution for a scalar differential equation of the type \[ (\phi(u'))'=h(t)g(u), \] where \(\phi:(-1,1)\to{\mathbb R}\) is a strictly increasing odd function, \(g:(\alpha,\beta)\to{\mathbb R}\) is continuous, while \(h:{\mathbb R}\to{\mathbb R}\) is locally integrable and \(T\)-periodic. Here, \(\alpha\) and \(\beta\) are two singularities satisfying \[ \lim_{x\to\alpha^+}g(x)=\lim_{x\to\beta^-}g(x)=+\infty. \] The function \(h\) needs to change sign, and a rather technical condition on its behaviour at the points where it changes sign is proposed, related to the order of the singularity \(\alpha\). The proof of the existence of a periodic solution is based on the Leray-Schauder continuation principle.
reviewed by: Alessandro Fonda
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 34B18
Mathematics Subject Classification ID: 34B16
Mathematics Subject Classification ID: 47N20
zbMATH DE Number: 6923442
zbMATH Keywords: singular differential equations
zbMATH Keywords: periodic solutions
zbMATH Keywords: Leray-Schauder continuation
MaRDI profile type: Publication
full work available at URL: dcds.2018211
OpenAlex ID: W2884052359
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Wikidata QID: Q129447481
DOI: 10.3934/DCDS.2018211
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description: scientific article; zbMATH DE number 6923442