School of Mathematics
Nanjing University of Aeronautics and Astronautics
Nanjing 211106, China
email: zwlou@nuaa.edu.cn
School of Mathematics
Nanjing University of Aeronautics and Astronautics
Nanjing 211106, China
email: 2414483646@qq.com
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.2023.02
Show me the PDF file (402 KB), TEX file for this article.
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Zhaowei Lou School of Mathematics Nanjing University of Aeronautics and Astronautics Nanjing 211106, China email: zwlou@nuaa.edu.cn |
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Youchao Wu School of Mathematics Nanjing University of Aeronautics and Astronautics Nanjing 211106, China email: 2414483646@qq.com |
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