AM  Vol.2 No.7 , July 2011
Multiple Periodic Solutions for Some Classes of First-Order Hamiltonian Systems
Author(s) Mohsen Timoumi
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.

Cite this paper
nullM. Timoumi, "Multiple Periodic Solutions for Some Classes of First-Order Hamiltonian Systems," Applied Mathematics, Vol. 2 No. 7, 2011, pp. 846-853. doi: 10.4236/am.2011.27114.
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