Boundedness of solutions for a class of impact oscillators with time-dependent polynomial potentials
type: Item
instance of: scholarly article
title: Boundedness of solutions for a class of impact oscillators with time-dependent polynomial potentials
zbMATH Open document ID: 1311.34070
author: Xiang Sun
author: Daxiong Piao
published in: Communications on Pure and Applied Analysis
publication date: 2013-11-13T00:00:00Z
full work available at URL: https://arxiv.org/abs/1301.6448
Mathematics Subject Classification ID: 34C11
Mathematics Subject Classification ID: 34C15
zbMATH DE Number: 6226495
zbMATH Keywords: impactor oscillators
zbMATH Keywords: boundedness of solutions
zbMATH Keywords: canonical transformation
zbMATH Keywords: time-dependent polynomial potentials
zbMATH Keywords: Moser's small twist theorem
MaRDI profile type: Publication
OpenAlex ID: W1970864778
arXiv ID: 1301.6448
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DOI: 10.3934/CPAA.2014.13.645
review text: By making use of action-angle variables and Moser's small twist theorem, the authors prove the boundedness of the solutions of a nonlinear impact oscillator with periodically time-dependent polynomial potential given by NEWLINE\[NEWLINE \ddot{x}+x^{2n+1}+\sum_{i=1}^{2n} p_i(t)x^i=0, NEWLINE\]NEWLINE with the impact condition NEWLINE\[NEWLINE x(t_0)=0\implies \dot{x}(t_0^+)=-\dot{x}(t_0^-), NEWLINE\]NEWLINE and the regularity assumption \(p_i\in C^5\).
description: scientific article; zbMATH DE number 6226495