Moser扭转定理在Lagrange稳定性中的应用(英文)

Lagrange Stability Via the Twist Theorem

本文利用Moser扭转定理证明了一类Duffing方程x’’+g(x)=e(t)的Lagrange稳定性,其中e(t)以1为周期,g:R→R具有下列性质:当x≥do时,g(x)是超线性的;当x≤-do时,g(x)是次线性的,其中do是一正常数.

We prove the Lagrange stability of solutions for a class of Duffing equations x + g(x) = e(t), where e(t) is of period 1, and g : IR → IR possesses the characters: g(x) is superlinear when x ≥ d0, d0 is a positive constant and g(x) is sublinear when x ≤-d0.