Differential and Integral Equations

Quasi-periodic solutions of a damped reversible oscillator at resonance

Anna Capietto, Walter Dambrosio, and Xinping Wang

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Abstract

We prove the existence of quasi-periodic solutions and of Aubry-Mather sets for a resonant reversible equation of the form $x^{\prime\prime} + ax^+ - bx^- +\varphi(x) +f(x,x',t)= p(t)$; the functions $p$ and $f$ are $2\pi$-periodic in $t$ and the perturbation $\varphi$ is bounded.

Article information

Source
Differential Integral Equations, Volume 22, Number 9/10 (2009), 1033-1046.

Dates
First available in Project Euclid: 20 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356019521

Mathematical Reviews number (MathSciNet)
MR2553069

Zentralblatt MATH identifier
1240.34221

Subjects
Primary: 34A36: Discontinuous equations
Secondary: 34C25: Periodic solutions 37E40: Twist maps 37E45: Rotation numbers and vectors

Citation

Capietto, Anna; Dambrosio, Walter; Wang, Xinping. Quasi-periodic solutions of a damped reversible oscillator at resonance. Differential Integral Equations 22 (2009), no. 9/10, 1033--1046. https://projecteuclid.org/euclid.die/1356019521


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