次线性非对称Duffing方程的不变环面

Invariant Tori of Sublinear Asymmetric Duffing Equations

利用Moser扭转定理,在一定的光滑性条件下,证明了次线性非对称Duffing方程x"+b(+x^(+))^((1/3))-b(x^(-))^((1/3))+φ(x)=p(t)无穷多不变环面的存在性,从而得到拉格朗日稳定性,其中扰动项φ(x)有界,而强迫项p(t)是周期函数.

By using Moser’s twist theorem,under some smoothness conditions,we prove the existence of infinitely many invariant tori and so the Lagrange stability for the sublinear asymmetric Duffing equations x"+b(+x^(+))^((1/3))-b(x^(-))^((1/3))+φ(x)=p(t),where the perturbation termφ(x)is bounded,while the forced term p(t)is periodic in t.