一类非对称Duffing方程的不变环面(英文)

Invariant Tori of Asymmetric Duffing Equations

证明了一类Duffing方程:(?)+g(x)=e(t).的不变环面的存在性,从而得出所有的解都是有界的,其中e(t)是以1为周期的函数,函数g:R→R具有性质:当x≥d_o时,g(x)是次线性的,当x≤-d_o时,g(x)是半线性的,d_o为一正常数.

We prove the existence of invariant tori and thus the boundedness of all solutions and the existence of quasiperiodic solutions for a class of Dulling equation x＋g （x）=e （t）. where e （t） is of period 1 ,and g ：R→R prossesses the characters ： g（x） is sublinear when x≥do,do is a positive constant and g（x） is semilinear when x≤-d0.