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

被引：4

作者：

Zhang, Xinli ^{[1
,2
]}

Peng, Yaqun ^{[1
]}

Piao, Daxiong ^{[1
]}

机构：

[1] Ocean Univ China, Sch Math Sci, Qingdao 266100, Peoples R China

[2] Qingdao Univ Sci & Technol, Sch Math & Phys, Qingdao 266061, Peoples R China

来源：

SCIENCE CHINA-MATHEMATICS | 2021年 / 64卷 / 05期

基金：

中国国家自然科学基金;

关键词：

quasi-periodic solutions; asymmetric oscillator; Littlewood’ s boundedness problem; invariant curves; BOUNDEDNESS;

D O I：

10.1007/s11425-018-9491-0

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we prove the existence of quasi-periodic solutions and boundeness of all 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 C39 is bounded for 0 <= i + j <= 35.

引用

页码：931 / 946

页数：16

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