Electronic Journal of Differential Equations, Vol. 2024 (2024), No. 02, pp. 1-20.

Title: A KAM theorem for degenerate infinite-dimensional reversible systems
       
Authors: Zhaowei Lou (Nanjing Univ. of Aeronautics and Astronautics, Nanjing, China)
         Youchao Wu  (Nanjing Univ. of Aeronautics and Astronautics, Nanjing, China)

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 03, 2024.
Math Subject Classifications: 37K55, 35B15.
Key Words: KAM theorem; infinite-dimensional reversible system; Russmann non-degeneracy condition.