Quasi-periodic Solutions for a Class of Higher Dimensional Beam Equation with Quasi-periodic Forcing

被引：2
|
作者：
Shi, Yanling [1 ]
Xu, Junxiang [2 ]
Xu, Xindong [2 ]
机构：
[1] Yancheng Inst Technol, Coll Math & Phys, Yancheng 224051, Peoples R China
[2] Southeast Univ, Dept Math, Nanjing 211189, Jiangsu, Peoples R China
来源：
JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS | 2019年 / 31卷 / 02期
关键词：
Beam equation; Quasi-periodic solution; Infinite dimensional KAM theory;
D O I：
10.1007/s10884-018-9657-z
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This work focuses on higher-dimensional quasi-periodically forced nonlinear beam equation. This means studying u(tt) + (-Delta + M xi)(2)u + e phi(t)(u + u(3)) = 0, x is an element of R-d, t is an element of R with periodic boundary conditions, where epsilon is a small positive parameter, phi(t) is a real analytic quasi-periodic function in t with frequency vector omega = (omega(1),omega(2),...,omega(m)). It is proved that there are many quasi-periodic solutions for the above equation via KAM theory.
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页码：745 / 763
页数：19
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