Moser扭转定理在Lgrange稳定性中的应用

摘要

We prove the Lagrange stability of solutions for a classof Duffing equations x +g(x) = e(t), where e(t) is of period 1, and g: IR → IR possesses the characters: g(x) is superlinearwhen x ≥ d0, d0 is a positive constant and g(x) is sublinear when x ≤ -d0.%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≥d0时,g(x)是超线性的;当x≤-d0时,9(x)是次线性的,其中d0悬一正常数.