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arXiv · 1701.05725

An infinite dimensional KAM theorem with application to two dimensional completely resonant beam equation

Jiansheng Geng·Shidi Zhou
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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.

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Jiansheng Geng, Shidi Zhou. 2017-01-20. An infinite dimensional KAM theorem with application to two dimensional completely resonant beam equation. https://doi.org/10.1063/1.5045780

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