Periodic solutions of forced isochronous oscillators at resonance
type: Item
instance of: scholarly article
title: Periodic solutions of forced isochronous oscillators at resonance
zbMATH Open document ID: 1021.34032
author: Didier Smets
author: Denis Bonheure
author: Christian Fabry
published in: Discrete and Continuous Dynamical Systems
publication date: 2003-10-09T00:00:00Z
review text: Sufficient conditions are given for the existence of a \(2\pi\)-periodic solution to the equation \[ x''(t)+V^\prime(x(t))+g(x(t))=p(t),\tag{*} \] if \(V:(a,+\infty)\to{\mathbb{R}}\) is a \(2\pi/k\)-isochronous, strictly convex potential with locally Lipschitzian derivative, \(g:(a,+\infty)\to{\mathbb{R}}\) is bounded and locally Lipschitzian, and \(p\) is \(L^1_{loc}\) and \(2\pi\)-periodic. Moreover, resonance conditions of either a singular or a nonsingular kind are imposed on \(F(t,x)=V^\prime(x)+g(x)-p(t)\). A nonexistence result is given as well.
Mathematics Subject Classification ID: 34C15
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 70K30
zbMATH DE Number: 1836296
zbMATH Keywords: isochronous potential
zbMATH Keywords: resonance
zbMATH Keywords: Landesman-Lazer conditions
MaRDI profile type: Publication
full work available at URL: dcds.2002.8.907
OpenAlex ID: W1991079636
DOI: 10.3934/DCDS.2002.8.907
description: scientific article; zbMATH DE number 1836296