Electron. J. Differential Equations, Vol. 2024 (2024), No. 02, pp. 1-20.

A KAM theorem for degenerate infinite-dimensional reversible systems

Zhaowei Lou, Youchao Wu

Abstract:
In this article, we establish a Kolmogorov-Arnold-Moser (KAM) theorem for degenerate infinite-dimensional reversible systems under a non-degenerate condition of Russmann type. This theorem broadens the scope of applicability of degenerate KAM theory, previously confined to Hamiltonian systems, by incorporating infinite-dimensional reversible systems. Using this theorem, we obtain the existence and linear stability of quasi-periodic solutions for a class of non-Hamiltonian but reversible beam equations with non-linearities in derivatives.

Submitted August 1, 2023. Published January 3, 2024.
Math Subject Classifications: 37K55, 35B15.
Key Words: KAM theorem; infinite-dimensional reversible system; Russmann non-degeneracy condition.
DOI: 10.58997/ejde.2024.02

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Zhaowei Lou
School of Mathematics
Nanjing University of Aeronautics and Astronautics
Nanjing 211106, China
email: zwlou@nuaa.edu.cn
Youchao Wu
School of Mathematics
Nanjing University of Aeronautics and Astronautics
Nanjing 211106, China
email: 2414483646@qq.com

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