Positive periodic solutions of second order nonlinear equations with indefinite weight: multiplicity results and complex dynamics
type: Item
instance of: scholarly article
title: Positive periodic solutions of second order nonlinear equations with indefinite weight: multiplicity results and complex dynamics
zbMATH Open document ID: 1237.34076
author: Alberto Boscaggin
author: Fabio Zanolin
published in: Journal of Differential Equations
publication date: 2012-01-16T00:00:00Z
review text: The authors prove the existence of a pair of positive \(T\)-periodic solutions as well as the existence of positive subharmonic solutions of any order and the presence of chaotic-like dynamics for the scalar second order ODE \[ u'' + a_{\lambda,\mu}(t)g(u)=0, \] where \(g(x)\) is a positive function on \(\mathbb R^+\), superlinear at zero and sublinear at infinity, and \(a_{\lambda,\mu}(t)\) is a \(T\)-periodic and sign indefinite weight of the form \(\lambda\) \(a^+(t)-\mu a^-(t)\), with \(\lambda, \mu>0\) and large.
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 34C28
zbMATH DE Number: 5998080
zbMATH Keywords: positive periodic solutions
zbMATH Keywords: Poincaré map
zbMATH Keywords: subharmonics
zbMATH Keywords: complex dynamics
reviewed by: Daniel Paşca
MaRDI profile type: Publication
full work available at URL: j.jde.2011.09.010
OpenAlex ID: W2055722004
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DOI: 10.1016/J.JDE.2011.09.010
description: scientific article; zbMATH DE number 5998080