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

Mohsen Timoumi

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DOI: 10.4236/am.2011.27114                

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≤a<1 , and e is a forcing term. For the proof, we use the Least Action Principle and a Generalized Saddle Point Theorem.

Keywords

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

Conflicts of Interest

The authors declare no conflicts of interest.

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