Hostname: page-component-78c5997874-94fs2 Total loading time: 0 Render date: 2024-11-19T09:48:21.348Z Has data issue: false hasContentIssue false
  • English
  • Français

Existence and multiplicity of periodic solutions for the Duffing equation with singularity

Published online by Cambridge University Press:  21 May 2007

Jing Xia  and
Zaihong Wang
Jing Xia
Affiliation:
Department of Mathematics, Capital Normal University, Beijing 100037, People's Republic of China ([email protected])
Zaihong Wang
Affiliation:
Department of Mathematics, Capital Normal University, Beijing 100037, People's Republic of China ([email protected])
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper, we consider the existence and multiplicity of periodic solutions for the Duffing equation $x''+g(x)=p(t)$ with a singularity. When the time map has oscillating properties, $g(x)$ possesses a singularity at the origin and tends to $+\infty$ as $x\to+\infty$ and other conditions hold. We obtain the existence of harmonic solutions and the multiplicity of subharmonic solutions of the given equation by using the phase-plane analysis methods and the generalized Poincaré–Birkhoff twist theorem.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 137 , Issue 3 , June 2007 , pp. 625 - 645
Copyright
2007 Royal Society of Edinburgh

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)