Quasi-periodic solutions for the general semilinear Duffing equations with asymmetric nonlinearity and oscillating potential  

作　　者：Xinli Zhang Yaqun Peng Daxiong Piao 

机构地区：[1]School of Mathematical Sciences,Ocean University of China,Qingdao 266100,China [2]School of Mathematics and Physics,Qingdao University of Science and Technology,Qingdao 266061,China

出　　处：《Science China Mathematics》2021年第5期931-946,共16页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China (Grant No.11571327)。

摘　　要：In this paper,we prove the existence of quasi-periodic solutions and the boundedness of all the solutions of the general semilinear quasi-periodic differential equation x′′+ax^(+)-bx^(-)=G_x(x,t)+f (t),where x^(+)=max{x,0},x^(-)=max{-x,0},a and b are two different positive constants,f(t) is C^(39) smooth in t,G(x,t)is C^(35) smooth in x and t,f (t) and G(x,t) are quasi-periodic in t with the Diophantine frequency ω=(ω_(1),ω_(2)),and D_(x)^(i)D_(t)^(j)G(x,t) is bounded for 0≤i+j≤35.

关 键 词：quasi-periodic solutions asymmetric oscillator Littlewood's boundedness problem invariant curves 

分 类 号：O175[理学—数学]