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Multiple Periodic Solutions for Some Classes of First-Order Hamiltonian Systems
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Abstract
Considering a decomposition <i>R<sup>2</sup>N</i>=<I>A⊕B</i> of <i>R<sup>2</sup>N</i> , we prove in this work, the existence of at least (1+dim<i>A</i>) geometrically distinct periodic solutions for the first-order Hamiltonian system <i>Jx'(t)+H'(t,x(t))+e(t)</i>=0 when the Hamiltonian <i>H(t,u+v)</i> is periodic in (<i>t,u</i>) and its growth at infinity in v is at most like or faster than |v|<sup>a</sup>, 0≤a<1 , and <i>e</i> is a forcing term. For the proof, we use the Least Action Principle and a Generalized Saddle Point Theorem.
KeywordsHamiltonian SystemsPartial NonlinearityMultiple Periodic SolutionsCritical Point Theory
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