Communications on Pure and Applied Analysis (CPAA)

The stability of the equilibrium for a perturbed asymmetric oscillator

Pages: 515 - 528, Volume 5, Issue 3, September 2006      doi:10.3934/cpaa.2006.5.515

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Xiong Li - Department of Mathematical Sciences, Beijing Normal University, Beijing 100875, China (email)

Abstract: In this paper we will derive some stability criteria for the equilibrium of a perturbed asymmetric oscillator

$\ddot x + a^+ x^+ - a^-$$ x^-$ $+ b(t)x^2+r(t,x)=0,$

where $a^+,a^-$ are two different positive numbers, $b(t)$ is a $2\pi$-periodic function, and the remaining term $r(t,x)$ is $2\pi$-periodic with respect to the time $t$ and dominated by the power $x^3$ in a neighborhood of the equilibrium $x=0$.

Keywords:  Stability, asymmetric oscillator, Moser small twist theorem.
Mathematics Subject Classification:  34D20; 34C15; 37J40.

Received: June 2005;      Revised: February 2006;      Available Online: June 2006.