PERIODIC SOLUTIONS TO NONLINEAR EULER-BERNOULLI BEAM EQUATIONS

被引：8

作者：

Chen, Bochao ^{[1
]}

Gao, Yixian ^{[2
]}

Li, Yong ^{[2
,3
]}

机构：

[1] Jilin Univ, Coll Math, Changchun 130012, Jilin, Peoples R China

[2] Northeast Normal Univ, Ctr Math & Interdisciplinary Sci, Sch Math & Stat, Changchun 130024, Jilin, Peoples R China

[3] Jilin Univ, Coll Math, Changchun 130024, Jilin, Peoples R China

来源：

COMMUNICATIONS IN MATHEMATICAL SCIENCES | 2019年 / 17卷 / 07期

基金：

中国博士后科学基金;

关键词：

Euler-Bernoulli beam equations; Variable coefficients; Periodic solutions; Nash-Moser iteration; DIMENSIONAL WAVE-EQUATION; COMPACT LIE-GROUPS; SCHRODINGER-EQUATIONS; KAM;

D O I：

10.4310/CMS.2019.v17.n7.a10

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Bending vibrations of thin beams and plates can be described by nonlinear Euler-Bernoulli beam equation with x-dependent coefficients. In this paper we demonstrate the existence of families of time-periodic solutions to such a model by virtue of a Lyapunov-Schmidt reduction together with a Nash-Moser method. This result holds for all parameters (epsilon,omega) in a Cantor set with asymptotically full measure as epsilon -> 0.

引用

页码：2005 / 2034

页数：30

共 40 条

[1] Resonances for Euler-Bernoulli operator on the half-line [J].

Badanin, Andrey ;

Korotyaev, Evgeny L. .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2017, 263 (01) :534-566

[2] Inverse problems and sharp eigenvalue asymptotics for Euler-Bernoulli operators [J].

Badanin, Andrey ;

Korotyaev, Evgeny .

INVERSE PROBLEMS, 2015, 31 (05)

[3] Forced vibrations of a nonhomogeneous string [J].

Baldi, Pietro ;

Berti, Massimiliano .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2008, 40 (01) :382-412

[4] Periodic solutions to one-dimensional wave equation with piece-wise constant coefficients [J].

Barbu, V ;

Pavel, NH .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1996, 132 (02) :319-337

[5] Periodic solutions to nonlinear one dimensional wave equation with X-dependent coefficients [J].

Barbu, V ;

Pavel, NH .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1997, 349 (05) :2035-2048

[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] An Abstract Nash-Moser Theorem and Quasi-Periodic Solutions for NLW and NLS on Compact Lie Groups and Homogeneous Manifolds [J].

Berti, Massimiliano ;

Corsi, Livia ;

Procesi, Michela .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2015, 334 (03) :1413-1454

[9] KAM for Reversible Derivative Wave Equations [J].

Berti, Massimiliano ;

Biasco, Luca ;

Procesi, Michela .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2014, 212 (03) :905-955

[10] NONLINEAR WAVE AND SCHRODINGER EQUATIONS ON COMPACT LIE GROUPS AND HOMOGENEOUS SPACES [J].

Berti, Massimiliano ;

Procesi, Michela .

DUKE MATHEMATICAL JOURNAL, 2011, 159 (03) :479-538

← 1 2 3 4 →