Applied Mathematics

Volume 2, Issue 7 (July 2011)

ISSN Print: 2152-7385   ISSN Online: 2152-7393

Google-based Impact Factor: 0.58  Citations  

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

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DOI: 10.4236/am.2011.27114    4,592 Downloads   8,545 Views  Citations




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.

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M. 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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