QUASI-PERIODIC SOLUTIONS OF NONLINEAR BEAM EQUATIONS WITH QUINTIC QUASI-PERIODIC NONLINEARITIES

被引：0

作者：

Tuo, Qiuju ^{[1
,2
]}

Si, Jianguo ^{[1
]}

机构：

[1] Shandong Univ, Sch Math, Jinan 250100, Shandong, Peoples R China

[2] Shandong Univ Finance & Econ, Sch Math & Quantitat Econ, Jinan 250014, Shandong, Peoples R China

来源：

ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS | 2015年

基金：

中国国家自然科学基金;

关键词：

Infinite dimensional Hamiltonian systems; KAM theory; HAMILTONIAN PERTURBATIONS; KAM THEOREM; STABILITY; SYSTEMS; TORI;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article, we consider the one-dimensional nonlinear beam equations with quasi-periodic quintic nonlinearities u(ll) + u(xxxx) + (B + epsilon phi(t))u(5) = 0 under periodic boundary conditions, where B is a positive constant, epsilon is a small positive parameter, phi(t) is a real analytic quasi-periodic function in t with frequency vector w = (w(1),w(2,)...,w(m)). It is proved that the above equation admits many quasi-periodic solutions by KAM theory and partial Birkhoff normal form.

引用

页数：20

共 30 条

[1]

[Anonymous], 2005, ANN MATH STUD

[2] Families of periodic orbits for some PDE's in higher dimensions [J].

Bambusi, D ;

Paleari, S .

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2002, 1 (02) :269-279

[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]

BAMBUSI D, 2000, ANN SCUOLA NORM SUP, V29, P823

[5] 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

[6] 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

[7]

Bourgain Jean, 1994, IMRN, V11, p475ff, DOI DOI 10.1155/S1073792894000516

[8]

DRABEK P, 1986, CZECH MATH J, V36, P434

[9] EXPONENTIAL ATTRACTORS FOR EXTENSIBLE BEAM EQUATIONS [J].

EDEN, A ;

MILANI, AJ .

NONLINEARITY, 1993, 6 (03) :457-479

[10] On Reducibility of Schrodinger Equations with Quasiperiodic in Time Potentials [J].

Eliasson, Hakan L. ;

Kuksin, Sergei B. .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2009, 286 (01) :125-135

← 1 2 3 →