The stability of the equilibrium for a perturbed asymmetric oscillator

Xiong Li

doi:10.3934/cpaa.2007.6.69

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2007, Volume 6, Issue 1: 69-82. Doi: 10.3934/cpaa.2007.6.69

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The stability of the equilibrium for a perturbed asymmetric oscillator

Xiong Li^1,

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

Received: February 28, 2006

Revised: September 30, 2006

Published: February 2007

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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 $x=0$.

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Mathematics Subject Classification: Primary: 34D20, 34C15; Secondary: 37J40.

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