Abstract
Abstract : A forced oscillation problem for a Hamiltonian equation on a torus is studied, If the dimension of the torus is equal to 2n, and if the period of the time dependent Hamiltonian equation is equal to 1, there are at least (2n+1) periodic solutions having period 1. In this paper it is shown, that, under an additional, necessary nondegeneracy condition such an equation possesses a periodic solution having minimal period T, for every sufficiently large prime number T. The proof uses the classical variational approach. It is based on the Morse theory for periodic solution to its Morse index and on an iteration formula for the winding number. Originator-supplied keywords included: Hamiltonian systems, Periodic solutions, Variational principles, Morse-type index theory, Winding number of a periodic solution, and Reprints.
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