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

• 作者: Xinli Zhang Yaqun Peng Daxiong Piao
• 来源期刊: 中国科学：数学（英文版）
• 年，卷（期）: 2021,（5）
• 所属期刊栏目: Articles
• 页码范围: 931-946
• 页数: 16页
• 语种: 英文

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-=Gx (x,t) + f (t),where x+ =max{x,0},x-=max{-x,0},a and b are two different positive constants,f(t) is C39 smooth in t,G(x,t)is C35 smooth in x and t,f(t) and G(x,t) are quasi-periodic in t with the Diophantine frequency ω =(ω1,ω2),and DixDjtG(x,t) is bounded for 0 ≤ i+j ≤ 35.