Abstract
We show, under an iterative condition, generalizing that of Ambrosetti–Rabinowitz and using a variational method, the existence of a T-periodic solution for the autonomous superquadratic second order Hamiltonian system with even potential
for any prescribed period \(T>0\). Moreover, under a certain symmetry condition, such a solution possesses T or T / 3 as its minimal period.
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Souissi, C. Generalized Ambrosetti–Rabinowitz condition for minimal period solutions of autonomous Hamiltonian systems. Arch. Math. 109, 73–82 (2017). https://doi.org/10.1007/s00013-017-1029-0
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DOI: https://doi.org/10.1007/s00013-017-1029-0