September  2006, 5(3): 515-528. doi: 10.3934/cpaa.2006.5.515

The stability of the equilibrium for a perturbed asymmetric oscillator

1. 

Department of Mathematical Sciences, Beijing Normal University, Beijing 100875, China

Received  June 2005 Revised  February 2006 Published  June 2006

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 $x=0$.

Citation: Xiong Li. The stability of the equilibrium for a perturbed asymmetric oscillator. Communications on Pure and Applied Analysis, 2006, 5 (3) : 515-528. doi: 10.3934/cpaa.2006.5.515
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