# American Institute of Mathematical Sciences

March  2007, 6(1): 69-82. doi: 10.3934/cpaa.2007.6.69

## The stability of the equilibrium for a perturbed asymmetric oscillator

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

Received  March 2006 Revised  October 2006 Published  December 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, 2007, 6 (1) : 69-82. doi: 10.3934/cpaa.2007.6.69
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