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The stability of the equilibrium for a perturbed asymmetric oscillator

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  • 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 $x=0$.

    Mathematics Subject Classification: 34D20; 34C15; 37J40.


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