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.

引用

页码：745 / 763

页数：19

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