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arXiv · 2401.00655

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

Yuming Xiao·Gaosheng Zhu
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Abstract

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.

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Yuming Xiao, Gaosheng Zhu. 2024-01-01. The minimal periodic solutions for superquadratic autonomous Hamiltonian systems without the Palais-Smale condition. https://arxiv.org/abs/2401.00655

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