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I. Ekeland and J. M. Lasry, “On the Number of Periodic Trajectories for a Hamiltonian Flow on a Convex Energy Surface,” Annals of Mathematics, Vol. 112, No. 2, 1980, pp. 283-319. doi:10.2307/1971148

has been cited by the following article:

• TITLE: Multiple Periodic Solutions for Some Classes of First-Order Hamiltonian Systems

  AUTHORS: Mohsen Timoumi

  KEYWORDS: Hamiltonian Systems, Partial Nonlinearity, Multiple Periodic Solutions, Critical Point Theory

  JOURNAL NAME: Applied Mathematics, Vol.2 No.7, July 8, 2011

  ABSTRACT: Considering a decomposition R2N=A⊕B of R2N , we prove in this work, the existence of at least (1+dimA) geometrically distinct periodic solutions for the first-order Hamiltonian system Jx'(t)+H'(t,x(t))+e(t)=0 when the Hamiltonian H(t,u+v) is periodic in (t,u) and its growth at infinity in v is at most like or faster than |v|a, 0≤ae is a forcing term. For the proof, we use the Least Action Principle and a Generalized Saddle Point Theorem.