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 method of Nehari manifold to directly deal with a frequently occurring problem where the Nehari set is not a manifold. (c) 2024 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.