Multiplicity of positive periodic solutions to superlinear repulsive singular equations
type: Item
instance of: scholarly article
title: Multiplicity of positive periodic solutions to superlinear repulsive singular equations
zbMATH Open document ID: 1074.34048
author: Daqing Jiang
author: Jifeng Chu
author: Meirong Zhang
published in: Journal of Differential Equations
publication date: 2005-05-04T00:00:00Z
review text: The authors study the existence and multiplicity of positive periodic solutions of the perturbed Hill equation \[ x''(t) + a(t)x(t) = f(t,x(t)), \] where \(f(t,x)\) has a repulsive singularity near \(x = 0\) and is superlinear near \(x = + \infty.\) This means, respectively, that \(\lim_{x \rightarrow 0^{+}} \;f(t,x) = + \infty,\) uniformly in \(t\) and that \(\lim_{x \rightarrow + \infty} \;f(t,x)/x = + \infty,\) uniformly in \(t.\) The proof is based on a nonlinear alternative of Leray-Schauder type and Krasnoselskii's fixed-point theorem on compression and expansion of cones.
reviewed by: Antonio Cañada
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 34B16
Mathematics Subject Classification ID: 47H10
Mathematics Subject Classification ID: 47H11
zbMATH DE Number: 2164777
zbMATH Keywords: periodic solutions
zbMATH Keywords: Hill equation
zbMATH Keywords: repulsive singular equations
zbMATH Keywords: multiplicity
zbMATH Keywords: superlinear
MaRDI profile type: Publication
full work available at URL: j.jde.2004.10.031
OpenAlex ID: W2097345663
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DOI: 10.1016/J.JDE.2004.10.031
description: scientific article; zbMATH DE number 2164777