Multiple periodic solutions with prescribed minimal period to second-order Hamiltonian systems


A new variational method based on Ekeland’s principle is introduced for the existence, localization and multiplicity of periodic solutions of a prescribed minimal period to second-order Hamiltonian systems. The oscillatory property at zero or infinity of only one component of the gradient of the potential function is sufficient for the existence of infinitely many solutions. Also, oscillating properties of several components of the gradient of the potential function yield sequences of solutions with some of the components tending in norm to zero and others to infinity.


Radu Precup
Department of Mathematics Babes-Bolyai University, Cluj-Napoca, Romania


second-order Hamiltonian system; periodic solution; minimal period; anti-periodic solution; multiple solutions; Ekeland’s variational principle.

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R. Precup, Multiple periodic solutions with prescribed minimal period to second-order Hamiltonian systems, Dyn. Syst. 29 (2014), no. 3, 424-438,



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