Notes and Comments. **The first results on subharmonics were obtained by Rabinowitz in 1985, who showed the existence of infinitely many subharmonics both**
in the subquadratic and superquadratic case, with suitable growth **conditions**
on H′**. Again the duality approach enabled Clarke and Ekeland in 1981 to treat**
the same problem in the convex-subquadratic case, with growth conditions on H **only.**
Recently, Michalek and Tarantello (see Michalek, R., Tarantello, G. 1982 and Tarantello, G. 1983) have obtained lower bound on the number of subharmonics of period kT **, based on symmetry considerations and on pinching estimates, as** in Sect. 5.2 of this article.

## References

Clarke, F., Ekeland, I.: Nonlinear oscillations and boundary-value problems for Hamiltonian systems. Arch. Rat. Mech. Anal. 78, 315–333 (1982)
Clarke, F., Ekeland, I.: Solutions p´eriodiques, du p´eriode donn´ee, des ´equations hamiltoniennes. Note CRAS Paris 287, 1013–1015 (1978)
Michalek, R., Tarantello, G.: Subharmonic solutions with prescribed minimal period for nonautonomous Hamiltonian systems. J. Diff. Eq. 72, 28–55 (1988)
Tarantello, G.: Subharmonic solutions for Hamiltonian systems via a ZZp **pseudoindex**
theory. Annali di Matematica Pura (to appear)
Rabinowitz, P.: On subharmonic solutions of a Hamiltonian system. Comm. Pure Appl.

Math. 33, 609–633 (1980)
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