The minimal periodic solutions for superquadratic autonomous Hamiltonian systems without the Palais-Smale condition

In this paper, we prove the existence of periodic solutions with any prescribed minimal period \(T>0\) for even second order Hamiltonian systems and convex first order Hamiltonian systems under the weak Nehari condition instead of Ambrosetti-Rabinowitz's. To this end, we shall develop the me...

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Bibliographic Details
Published in:arXiv.org 2024-01
Main Authors: Xiao, Yuming, Zhu, Gaosheng
Format: Article
Language:English
Subjects:
Hamiltonian functions
Manifolds (mathematics)
Online Access:Get full text
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Summary:In this paper, we prove the existence of periodic solutions with any prescribed minimal period \(T>0\) for even second order Hamiltonian systems and convex first order Hamiltonian systems under the weak Nehari condition instead of Ambrosetti-Rabinowitz's. To this end, we shall develop the method of Nehari manifold to directly deal with a frequently occurring problem where the Nehari manifold is not a manifold.
ISSN:2331-8422