Subharmonic solutions for hamiltonian systems via a ℤ p pseudoindex theory
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Volume 15 (1988) no. 3, p. 357-409 
@article{ASNSP_1988_4_15_3_357_0,
     author = {Tarantello, Gabriella},
     title = {Subharmonic solutions for hamiltonian systems via a $\mathbb {Z}\_p$ pseudoindex theory},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 15},
     number = {3},
     year = {1988},
     pages = {357-409},
     zbl = {0755.34035},
     mrnumber = {1015800},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_1988_4_15_3_357_0}
}

Tarantello, Gabriella. Subharmonic solutions for hamiltonian systems via a $\mathbb {Z}_p$ pseudoindex theory. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Volume 15 (1988) no. 3, pp. 357-409. http://www.numdam.org/item/ASNSP_1988_4_15_3_357_0/

[1] V. Benci: A geometrical index for the group S1 and some applications to the study of periodic solutions of ordinary differential equations, Comm. Pure Appl. Math. 34 (1981), pp. 393-432. | MR 615624 | Zbl 0447.34040

[2] V. Benci: On the critical point theory for indefinite functionals in the presence of symmetries, Trans. Am. Math. Soc. 274 (1982), pp. 533-572. | MR 675067 | Zbl 0504.58014

[3] V. Benci - D. Fortunato: Subharmonic solutions of prescribed minimal period for nonautonomous differential equations, preprint. | MR 902625

[4] H. Berestycki - J.M. Lasry - G. Mancini - B. Ruf: Existence of multiple periodic orbits on star-shaped Hamiltonian surfaces, Comm. Pure Appl. Math. 38 (1985), pp. 253-289. | MR 784474 | Zbl 0569.58027

[5] G.D. Birkhoff - D.C. Lewis: On the periodic motion near a given periodic motion of a dynamical system, Ann. Mat. Pure Appl. 12 (1933), pp. 117-133. | JFM 59.0733.05 | Zbl 0007.37104

[6] F. Clarke - I. Ekeland: Nonlinear oscillations and boundary value problems for Hamiltonian systems, Archive Rat. Mech. Anal. 78 (1982), pp. 315-333. | MR 653545 | Zbl 0514.34032

[7] I. Ekeland - H. Hofer: Subharmonics for convex nonautonomous Hamiltonian systems, Comm. Pure Appl. Math. 40 (1987), pp. 1-36. | MR 865356 | Zbl 0601.58035

[8] I. Ekeland - H. Hofer: Periodic solutions with prescribed minimal period for convex autonomous Hamiltonian systems, Inventions Math. 81 (1985), pp. 155-188. | MR 796195 | Zbl 0594.58035

[9] E. Fadell - S. Husseini - P.H. Rabinowiz: Borsuk-Ulam theorem for arbitrary S1 actions and applications, M.R.C. Tech. Summary report 2301 Madison, WI 53706.

[10] M. Girardi - M. Matzeu: Solutions of minimal period for a class of nonconvex Hamiltonian systems and application to the fixed Energy problem, Nonlinear Analysis T.M.A. Vol. 10 n. 34 (1986), pp. 371-382. | MR 836672 | Zbl 0607.70018

[11] M. Girardi - M. Matzeu: Periodic solutions of convex autonomous Hamiltonian systems with quadratic growth at the origin and superquadratic at infinity, preprint.

[12] R. Michalek: A Z P Borsuk-Ulam theorem and Index theory with a multiplicity result, preprint.

[13] R. Michalek - G. Tarantello: Subharmonic solutions with prescribed minimal period for nonautonomous Hamiltonian systems, J. Diff. Eq. in press. | Zbl 0645.34038

[14] J. Moser: Proof of a generalized fixed point theorem due to G.D. Birkhoff, Lecture notes in Mathematics, 597 Springer Verlag, New York 1977. | MR 494305

[15] L. Nirenberg: Comments on nonlinear problems, Conference Proceedings, Catania Sept. 1981. | MR 736798

[16] P.H. Rabinowitz: On subharmonic solutions of Hamiltonian systems, Comm. Pure Appl. Math. 33 (1980), pp. 609-633. | MR 586414 | Zbl 0425.34024

[17] P.H. Rabinowitz: Variational methods for nonlinear eigenvalue problem, in Eigenvalue of nonlinear problems, ed. G. Prodi, edizioni Cremonese Rome 1974. | MR 464299

[18] H. Weyl: The theory of groups and quantum mechanics, Dover, New York, 1950. | Zbl 0041.56804

[19] V. Benci - D. Fortunato: A "Birkhoff-Lewis" type result for a class of Hamiltonian systems, preprint. | MR 915996