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Semi-stable and extremal solutions of reaction equations involving the $p$-Laplacian
The stability of the equilibrium for a perturbed asymmetric oscillator
| 1. | Department of Mathematical Sciences, Beijing Normal University, Beijing 100875 |
$\ddot x +a^+ x^+ - a^-$ $x^-$ $+ b(t)x^2+r(t,x)=0,$
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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