An infinite dimensional KAM theorem with application to two dimensional completely resonant beam equation
Dynamical Systems
2018-08-15 v1
Abstract
In this paper we consider the completely resonant beam equation on \T^2 with cubic nonlinearity on a subspace of L^2 (\T^2) which will be explained later. We establish an abstract infinite dimensional KAM theorem and apply it to the completely resonant beam equation. We prove the existence of a class of Whitney smooth small amplitude quasi-periodic solutions corresponding to finite dimensional tori.
Keywords
Cite
@article{arxiv.1701.05725,
title = {An infinite dimensional KAM theorem with application to two dimensional completely resonant beam equation},
author = {Jiansheng Geng and Shidi Zhou},
journal= {arXiv preprint arXiv:1701.05725},
year = {2018}
}
Comments
26 pages