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.