Bifurcations from infinity in asymmetric nonlinear oscillators
type: Item
instance of: scholarly article
title: Bifurcations from infinity in asymmetric nonlinear oscillators
zbMATH Open document ID: 0979.34033
DOI: 10.1007/PL00001421
author: Alessandro Fonda
author: Christian Fabry
published in: NoDEA. Nonlinear Differential Equations and Applications
publication date: 2002-02-03T00:00:00Z
review text: The authors study the existence of large-amplitude periodic and almost-periodic solutions to second-order differential equations with asymmetric nonlinearities of the following type \[ x^{\prime \prime }+\mu x^{+}-\upsilon x^{-}=g(t,x,x',\varepsilon) \] with \(\mu >0,\) \(\upsilon >0,\quad \frac{1}{\sqrt{ \mu }}+\frac{1}{\sqrt{\upsilon }}=\frac{2}{n}\) for some positive \(n\), and \(\varepsilon \) is a small parameter. The pair \(\left( \mu ,\upsilon \right) \) belongs to the \(n\)th-Fucik spectrum. The authors call this situation nonlinear resonance. They consider the problem of bifurcation from infinity when \(\varepsilon \) is near zero. The paper is well organized and the results are very interesting.
reviewed by: Abdelkader Boucherif
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 37G10
Mathematics Subject Classification ID: 34C27
zbMATH DE Number: 1439281
zbMATH Keywords: differential equations
zbMATH Keywords: asymmetric nonlinearities
zbMATH Keywords: bifurcation from infinity
zbMATH Keywords: large-amplitude periodic and almost-periodic solutions
zbMATH Keywords: Fucik spectrum
MaRDI profile type: Publication
full work available at URL: pl00001421
OpenAlex ID: W2031462491
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description: scientific article; zbMATH DE number 1439281