Small amplitude periodic solutions of Klein-Gordon equations

被引：3
作者：
Lu, Nan [1 ]
机构：
[1] Auburn Univ, Dept Math & Stat, 221 Parker Hall, Auburn, AL 36849 USA
来源：
ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE | 2017年 / 34卷 / 05期
关键词：
Klein-Gordon equation; Periodic solution; Nash-Moser iteration; NONLINEAR-WAVE-EQUATIONS; EXPONENTIAL STABILITY; HAMILTONIAN-SYSTEMS; CANTOR FAMILIES; VIBRATIONS;
D O I：
10.1016/j.anihpc.2016.10.002
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider a class of nonlinear Klein Gordon equations u(tt) = u(xx) - u + f(u) and obtain a family of small amplitude periodic solutions, where the temporal and spatial period have different scales. The proof is based on a combination of Lyapunov-Schmidt reduction, averaging and Nash-Moser iteration. (C) 2016 Elsevier Masson SAS. All rights reserved.
引用
收藏
页码：1255 / 1272
页数：18
相关论文
共 30 条
[1]  
[Anonymous], 2006, Ordinary Differential Equations with Applications
[2]  
[Anonymous], 1968, COMMUN PUR APPL MATH, DOI DOI 10.1002/CPA.3160220103
[3]   Quasi-periodic solutions of the equation vtt-vxx+v3=f(v) [J].
Baldi, P .
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2006, 15 (03) :883-903
[4]   A property of exponential stability in nonlinear wave equations near the fundamental linear mode [J].
Bambusi, D ;
Nekhoroshev, NN .
PHYSICA D-NONLINEAR PHENOMENA, 1998, 122 (1-4) :73-104
[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]   An abstract Nash-Moser theorem with parameters and applications to PDEs [J].
Berti, M. ;
Bolle, P. ;
Procesi, M. .
ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2010, 27 (01) :377-399
[7]   Cantor families of periodic solutions of wave equations with Ck nonlinearities [J].
Berti, Massimiliano ;
Bolle, Philippe .
NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 2008, 15 (1-2) :247-276
[8]   Cantor families of periodic solutions for completely resonant wave equations [J].
Berti, Massimiliano ;
Bolle, Philippe .
FRONTIERS OF MATHEMATICS IN CHINA, 2008, 3 (02) :151-165
[9]   Sobolev Periodic Solutions of Nonlinear Wave Equations in Higher Spatial Dimensions [J].
Berti, Massimiliano ;
Bolle, Philippe .
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2010, 195 (02) :609-642
[10]  
BREZIS H, 1978, COMMUN PUR APPL MATH, V31, P1
123