数学进展
數學進展
수학진전
ADVANCES IN MATHEMATICS
2004年
4期
477-488
,共12页
拟周期运动%Duffing方程%Moser扭转定理%Lagrange稳定性
擬週期運動%Duffing方程%Moser扭轉定理%Lagrange穩定性
의주기운동%Duffing방정%Moser뉴전정리%Lagrange은정성
quasiperiodic motion%Duffing equation%Moser's small twist theorem%Lagrange stability
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.
本文利用Moser扭轉定理證明瞭一類Duffing方程x″+g(x)=e(t)的Lagrange穩定性,其中e(t)以1為週期,g:R→R具有下列性質:噹x≥d0時,g(x)是超線性的;噹x≤-d0時,9(x)是次線性的,其中d0懸一正常數.
본문이용Moser뉴전정리증명료일류Duffing방정x″+g(x)=e(t)적Lagrange은정성,기중e(t)이1위주기,g:R→R구유하렬성질:당x≥d0시,g(x)시초선성적;당x≤-d0시,9(x)시차선성적,기중d0현일정상수.
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.
