Quasi-periodic solutions to nonlinear beam equations on compact Lie groups with a multiplicative potential

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:264

Article

Chen, Bochao¹  Gao, Yixian¹  Jiang, Shan¹  Li, Yong^1,2 

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

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

关键词: Beam equations;    Compact Lie groups;    Multiplicative potential;    Quasi-periodic solutions;    Nash-Moser iteration;   

DOI  :  10.1016/j.jde.2018.02.005

来源: Elsevier

【 摘 要 】

The goal of this work is to study the existence of quasi-periodic solutions to nonlinear beam equations with a multiplicative potential. The nonlinearity is required to only finitely differentiable and the frequency is along a pre-assigned direction. The result holds on any compact Lie group or homogeneous manifold with respect to a compact Lie group, which includes standard torus T-d, special orthogonal group SO(d), special unitary group SU(d), spheres S-d and the real and complex Grassmannians. The proof is based on a differentiable Nash-Moser iteration scheme. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free