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Subharmonic of not uniformly partially coercive Hamiltonian systems

Timoumi M.

Demonstratio Mathematica

2008

Vol. 41, nr 1

233-248

In this work, we prove the existence of multiple periodic and subharmonic solutions of the Hamiltonian system [..] when the Hamiltonian H is periodic in a part of the variables and locally coercive in the other part; that is, there exists a decomposition [...] for almost every t in some non empty open subset C of [O, T]. For the resolution, we use an analogy of Egorov's Theorem and a Generalized Saddle Point Theorem.