The stability of the equilibrium for a perturbed asymmetric oscillator
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.
Received: June 2005; Revised: February 2006; Published: June 2006.
2012 Impact Factor.589