The Lyapunov Stability for the Linear and Nonlinear Damped Oscillator with Time‐Periodic Parameters

Jifeng Chu and Ting Xia

Abstract and Applied Analysis, 2010, vol. 2010, issue 1

Abstract: Let a(t), b(t) be continuous T‐periodic functions with ∫0Tb(t)dt=0. We establish one stability criterion for the linear damped oscillator x′′ + b(t)x′ + a(t)x = 0. Moreover, based on the computation of the corresponding Birkhoff normal forms, we present a sufficient condition for the stability of the equilibrium of the nonlinear damped oscillator x′′ + b(t)x′ + a(t)x + c(t)x2n−1 + e(t, x) = 0, where n ≥ 2, c(t) is a continuous T‐periodic function, e(t, x) is continuous T‐periodic in t and dominated by the power x2n in a neighborhood of x = 0.

Date: 2010
References: Add references at CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1155/2010/286040

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2010:y:2010:i:1:n:286040

Access Statistics for this article

More articles in Abstract and Applied Analysis from John Wiley & Sons
Bibliographic data for series maintained by Wiley Content Delivery ().