Subharmonics of nonconvex Hamiltonian systems (Q1969088)
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scientific article; zbMATH DE number 1415708
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Subharmonics of nonconvex Hamiltonian systems |
scientific article; zbMATH DE number 1415708 |
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Subharmonics of nonconvex Hamiltonian systems (English)
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16 March 2000
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The author deals with the Hamiltonian system (1) \(\dot u= J\nabla H(t,u)\) where \(J= \left( \begin{smallmatrix} O &-I\\ I &O \end{smallmatrix} \right)\) is the standard symplectic matrix. Under some natural assumptions on \(H(t,u)\) the author derives the existence of subharmonic solutions for an unbounded noncovnex Hamiltonian with a bounded gradient. To this end the author uses a generalized saddle point theorem.
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Hamiltonian system
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subharmonic solution
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generalized saddle theorem
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