Quasi-periodic solutions of a non-autonomous wave equations with quasi-periodic forcing

被引：20
作者：
Si, Jianguo [1 ]
机构：
[1] Shandong Univ, Sch Math, Jinan 250100, Shandong, Peoples R China
来源：
JOURNAL OF DIFFERENTIAL EQUATIONS | 2012年 / 252卷 / 10期
基金：
中国国家自然科学基金;
关键词：
Infinite-dimensional Hamiltonian systems; KAM theory; Non-autonomous wave equations; Quasi-periodic solutions; Invariant torus; HAMILTONIAN PERTURBATIONS; FORCED VIBRATIONS; STABILITY; FAMILIES; SYSTEMS;
D O I：
10.1016/j.jde.2012.01.034
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we prove existence of small amplitude quasi-periodic solutions for a non-autonomous, quasi-periodically forced nonlinear wave equations with periodic spatial boundary conditions via RAM theory. (C) 2012 Elsevier Inc. All rights reserved.
引用
收藏
页码：5274 / 5360
页数：87
相关论文
共 32 条
[1]  
[Anonymous], 1993, LECT NOTES MATH
[2]   Families of periodic solutions of resonant PDEs [J].
Bambusi, D ;
Paleari, S .
JOURNAL OF NONLINEAR SCIENCE, 2001, 11 (01) :69-87
[3]   Time quasi-periodic unbounded perturbations of Schrodinger operators and KAM methods [J].
Bambusi, D ;
Graffi, S .
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2001, 219 (02) :465-480
[4]   Quasi-periodic solutions of completely resonant forced wave equations [J].
Berti, M ;
Procesi, M .
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2006, 31 (06) :959-985
[5]   Periodic solutions of nonlinear wave equations with general nonlinearities [J].
Berti, M ;
Bolle, P .
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2003, 243 (02) :315-328
[6]  
Berti M, 2005, REND LINCEI-MAT APPL, V16, P117
[7]   Forced vibrations of wave equations with non-monotone nonlinearities [J].
Berti, Massimiliano ;
Biasco, Luca .
ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2006, 23 (04) :439-474
[8]   Cantor families of periodic solutions for completely resonant nonlinear wave equations [J].
Berti, Massimiliano ;
Bolle, Philippe .
DUKE MATHEMATICAL JOURNAL, 2006, 134 (02) :359-419
[9]   Stability of zero solutions of essentially nonlinear one-degree-of-freedom Hamiltonian and reversible systems [J].
Bibikov, YN .
DIFFERENTIAL EQUATIONS, 2002, 38 (05) :609-614
[10]  
Bogoljubov N.N., 1976, METHODS ACCELERATED
1234