Subharmonic solutions for hamiltonian systems via a ${\mathbb{Z}}_p$ pseudoindex theory

 Access to full text

 Full (PDF)

1. [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. Zbl0447.34040MR615624
2. [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. Zbl0504.58014MR675067
3. [3] V. Benci - D. Fortunato: Subharmonic solutions of prescribed minimal period for nonautonomous differential equations, preprint. Zbl0663.70028MR902625
4. [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. Zbl0569.58027MR784474
5. [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. Zbl0007.37104JFM59.0733.05
6. [6] F. Clarke - I. Ekeland: Nonlinear oscillations and boundary value problems for Hamiltonian systems, Archive Rat. Mech. Anal.78 (1982), pp. 315-333. Zbl0514.34032MR653545
7. [7] I. Ekeland - H. Hofer: Subharmonics for convex nonautonomous Hamiltonian systems, Comm. Pure Appl. Math.40 (1987), pp. 1-36. Zbl0601.58035MR865356
8. [8] I. Ekeland - H. Hofer: Periodic solutions with prescribed minimal period for convex autonomous Hamiltonian systems, Inventions Math.81 (1985), pp. 155-188. Zbl0594.58035MR796195
9. [9] E. Fadell - S. Husseini - P.H. Rabinowiz: Borsuk-Ulam theorem for arbitrary S1 actions and applications, M.R.C. Tech. Summary report 2301Madison, WI 53706. 
10. [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. Zbl0607.70018MR836672
11. [11] M. Girardi - M. Matzeu: Periodic solutions of convex autonomous Hamiltonian systems with quadratic growth at the origin and superquadratic at infinity, preprint. 
12. [12] R. Michalek: A Z P Borsuk-Ulam theorem and Index theory with a multiplicity result, preprint. Zbl0688.58040
13. [13] R. Michalek - G. Tarantello: Subharmonic solutions with prescribed minimal period for nonautonomous Hamiltonian systems, J. Diff. Eq. in press. Zbl0645.34038
14. [14] J. Moser: Proof of a generalized fixed point theorem due to G.D. Birkhoff, Lecture notes in Mathematics, 597Springer Verlag, New York1977. Zbl0358.58009MR494305
15. [15] L. Nirenberg: Comments on nonlinear problems, Conference Proceedings, Catania Sept. 1981. MR736798
16. [16] P.H. Rabinowitz: On subharmonic solutions of Hamiltonian systems, Comm. Pure Appl. Math.33 (1980), pp. 609-633. Zbl0425.34024MR586414
17. [17] P.H. Rabinowitz: Variational methods for nonlinear eigenvalue problem, in Eigenvalue of nonlinear problems, ed. G. Prodi, edizioni CremoneseRome1974. Zbl0278.35040MR464299
18. [18] H. Weyl: The theory of groups and quantum mechanics, Dover, New York, 1950. Zbl0041.56804
19. [19] V. Benci - D. Fortunato: A "Birkhoff-Lewis" type result for a class of Hamiltonian systems, preprint. MR915996