Nonautonomous Hamiltonian systems of the form
where is the standard symplectic matrix
and the Hamiltonian is a -periodic (in the second variable) function, i.e. , for all is considered. Precisely, for any given integer the existence of multiple periodic (subharmonical) solutions of Eq. (1) is investigated.
It is known, that under rather general assumptions on for any integer the subharmonic problem (1) was shown to have a distinct solution and if has subquadratic or superquadratic growth at the origin and at infinity then the minimal period of tends towards infinity as .
Some new multiplicity results are obtained for convex with subquadratic growth at the origin and at infinity. Roughly speaking, it is shown that there exist many subharmonics with exact minimal period provided (the smallest prime factor of is sufficiently large. Using a dual variational method the author answers the question whether the number of solutions of (1) with minimal period tends towards infinity as .