聊城大学学报(自然科学版)
聊城大學學報(自然科學版)
료성대학학보(자연과학판)
JOURNAL OF LIAOCHENG TEACHERS UNIVERSITY(NATURAL SCIENCE EDITION)
2008年
1期
36-40,80
,共6页
拟周期解%Duffing方程%Moser小扭转定理
擬週期解%Duffing方程%Moser小扭轉定理
의주기해%Duffing방정%Moser소뉴전정리
Quasiperiodic solutions%Duffing equations%Moser's small twist theorem
证明了一类Duffing方程:(x¨)+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≥d0时,g(x)是次线性的,当x≤-d0时,g(x)是半线性的,d0为一正常数.
證明瞭一類Duffing方程:(x¨)+g(x)=e(t).的不變環麵的存在性,從而得齣所有的解都是有界的,其中e(t)是以1為週期的函數,函數g:R→R具有性質:噹x≥d0時,g(x)是次線性的,噹x≤-d0時,g(x)是半線性的,d0為一正常數.
증명료일류Duffing방정:(x¨)+g(x)=e(t).적불변배면적존재성,종이득출소유적해도시유계적,기중e(t)시이1위주기적함수,함수g:R→R구유성질:당x≥d0시,g(x)시차선성적,당x≤-d0시,g(x)시반선성적,d0위일정상수.
We prove the existence of invariant tori and thus the boundedness of all solutions and the existence of quasiperiodic solutions for a class of Duffing 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≥d0,d0 is a positive constant and g(x) is semilinear when x≤-d0.