A topological approach to periodic oscillations related to the Liebau phenomenon
type: Item
instance of: scholarly article
title: A topological approach to periodic oscillations related to the Liebau phenomenon
zbMATH Open document ID: 1309.34031
author: Milan Tvrdý
author: J. Ángel Cid
author: Gennaro Infante
author: Mirosława Zima
published in: Journal of Mathematical Analysis and Applications
publication date: 2014-11-19T00:00:00Z
full work available at URL: https://arxiv.org/abs/1408.0130
review text: The authors give some sufficient conditions for existence, non-existence and localization of positive solutions for the periodic boundary value problem \[ x''(t)+ax'(t)=r(t)x^\alpha(t)-s(t)x^\beta(t), x(0)=x(T), x'(0)=x'(T), \] where \(a\geq 0\), \(r\), \(s\in C[0, T]\), \(0<\alpha<\beta <1\). This problem is related to the Liebau phenomenon. Their approach is of topological nature and relies on the Krasnosel'skiǐ-Guo theorem on cone expansion and compression. Their results improve and complement earlier ones in the literature.
Mathematics Subject Classification ID: 34B18
Mathematics Subject Classification ID: 37N20
Mathematics Subject Classification ID: 47N20
Mathematics Subject Classification ID: 34B27
zbMATH DE Number: 6370952
zbMATH Keywords: valveless pumping
zbMATH Keywords: periodic boundary value problem
zbMATH Keywords: Krasnosel'skii-Guo fixed point theorem
zbMATH Keywords: Green's function
reviewed by: Ruyun Ma
describes a project that uses: Green
MaRDI profile type: Publication
OpenAlex ID: W2028928257
arXiv ID: 1408.0130
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DOI: 10.1016/J.JMAA.2014.10.054
description: scientific article