The minimal period problem of classical hamiltonian systems with even potentials
Annales de l'I.H.P. Analyse non linéaire, Volume 10 (1993) no. 6, p. 605-626
@article{AIHPC_1993__10_6_605_0,
     author = {Long, Yiming},
     title = {The minimal period problem of classical hamiltonian systems with even potentials},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     publisher = {Gauthier-Villars},
     volume = {10},
     number = {6},
     year = {1993},
     pages = {605-626},
     zbl = {0804.58018},
     mrnumber = {1253604},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_1993__10_6_605_0}
}
Long, Yiming. The minimal period problem of classical hamiltonian systems with even potentials. Annales de l'I.H.P. Analyse non linéaire, Volume 10 (1993) no. 6, pp. 605-626. http://www.numdam.org/item/AIHPC_1993__10_6_605_0/

[1] H. Amann and E. Zehnder, Nontrivial Solutions for a Class of Nonresonance Problems and Applications to Nonlinear Deferential Equations, Ann. Scuola Norm. Super. Pisa, Vol. 7, 1980, pp. 539-603. | Numdam | Zbl 0452.47077

[2] A. Ambrosetti and V. Coti Zelati, Solutions with Minimal Period for Hamiltonian Systems in a Potential Well, Ann. Inst. Henri-Poincaré, Anal. non linéaire, Vol. 4, 1987, pp. 275-296. | Numdam | Zbl 0623.58013

[3] A. Ambrosetti and G. Mancini, Solutions of Minimal Period for a Class of Convex Hamiltonian Systems, Math. Ann., Vol. 255, 1981, pp. 405-421. | Zbl 0466.70022

[4] A. Ambrosetti and P. Rabinowitz, Dual Variational Methods in Critical Point Theory, J. Funct. Anal., Vol. 14, 1973, pp. 343-387. | Zbl 0273.49063

[5] F. Clarke and I. Ekeland, Hamiltonian Trajectories Having Prescribed Minimal Period, Comm. Pure Appl. Math., Vol. 33, 1980, pp. 103-116. | Zbl 0403.70016

[6] S. Deng, Minimal Period Solutions of a Class of Hamiltonian Equation Systems, Acta Math. Sinica, Vol. 27, 1984, pp. 664-675. | Zbl 0577.58015

[7] I. Ekeland, Une théorie de Morse pour les systèmes hamiltoniens convexes, Ann. I.H.P. Anal. non linéaire, Vol. 1, 1984, pp. 19-78. | Numdam | Zbl 0537.58018

[8] I. Ekeland, An Index Theory for Periodic Solutions of Convex Hamiltonian Systems, Proc. Symp. in Pure Math., Vol. 45, 1986, pp. 395-423. | Zbl 0596.34023

[9] I. Ekeland, Convexity Methods in Hamiltonian Mechanics, Springer, Berlin, 1990. | Zbl 0707.70003

[10] I. Ekeland and H. Hofer, Periodic Solutions with Prescribed Period for Convex Autonomous Hamiltonian Systems, Inven. Math., Vol. 81, 1985, pp. 155-188. | Zbl 0594.58035

[11] N. Ghoussoub, Location, Multiplicity and Morse Indices of Min-Max Critical Points, Preprint. | Zbl 0736.58011

[12] M. Girardi and M. Matzeu, Some Results on Solutions of Minimal Period to Superquadratic Hamiltonian Equations, Nonlinear Anal. T.M.A., Vol. 7, 1983, pp. 475-482. | Zbl 0512.70021

[13] M. Girardi and M. Matzeu, Solutions of Minimal Period for a Class of Nonconvex Hamiltonian Systems and Applications to the Fixed Energy Problem, Nonlinear Anal. T.M.A., Vol. 10, 1986, pp. 371-382. | Zbl 0607.70018

[14] M. Girardi and M. Matzeu, Periodic Solutions of Convex Autonomous Hamiltonian Systems with a Quadratic Growth at the Origin and Superquadratic at Infinity, Ann. Mat. pura ed appl., Vol. 147, 1987, pp. 21-72. | Zbl 0631.58014

[15] M. Girardi and M. Matzeu, Dual Morse Index Estimates for Periodic Solutions of Hamiltonian Systems in Some Nonconvex Superquadratic Case, Nonlinear Anal. T.M.A., Vol. 17, 1991, pp. 481-497. | Zbl 0779.34033

[16] M. Girardi and M. Matzeu, Essential Critical Points of Linking Type and Solutions of Minimal Period to Superquadratic Hamiltonian Systems, Preprint, 1991. | Zbl 0776.58030

[17] H. Hofer, A Geometric Description of the Neighbourhood of a Critical Point Given by the Mountain-Pass Theorem, J. London Math. Soc., Vol. 31, 1985, pp. 556-570. | Zbl 0573.58007

[18] M.A. Krasnosel'Skii, Topological Methods in the Theory of Nonlinear Integral Equations, Pergamon Press, Oxford, 1963. | Zbl 0111.30303

[19] A. Lazer and S. Solimini, Nontrivial Solutions of Operator Equations and Morse Indices of Critical Points of Min-Max Type, Nonlinear Anal. T.M.A., Vol. 12, 1988, pp. 761-775. | Zbl 0667.47036

[20] Y. Long, The Minimal Period Problem of Periodic Solutions for Autonomous Superquadratic Second Order Hamiltonian System, Preprint of Nankai, Inst. Math. Nankai Univ., April 1991. Revised version, Preprint of F.I. Math. E.T.H.-Zürich, Nov. 1991, May 1992, J. Diff. Equa. (to appear).

[21] P. Rabinowitz, Periodic Solutions of Hamiltonian Systems, Comm. Pure Appl. Math., Vol. 31, 1978, pp. 157-184. | Zbl 0358.70014

[22] P. Rabinowitz, Periodic Solutions of Hamiltonian Systems: a Survey, S.I.A.M. J. Math. Anal., Vol. 13, 1982, pp. 343-352. | Zbl 0521.58028

[23] P. Rabinowitz, Minimax Methods in Critical Point Theory with Applications to Differential Equations, C.B.M.S. Reg. Conf. Ser. in Math., No. 65, Amer. Math. Soc., 1986. | Zbl 0609.58002

[24] P. Rabinowitz, On the Existence of Periodic Solutions for a class of Symmetric Hamiltonian Systems, Nonlinear Anal. T.M.A., Vol. 11, 1987, pp. 599-611.

[25] S. Solimini, Morse Index Estimates in Min-Max Theorems, Manus. Math., Vol. 63, 1989, pp. 421-453. | Zbl 0685.58010

[26] G. Tian, On the Mountain-Pass Lemma, Kexue Tongbao, Vol. 29, 1984, pp. 1151-1154. | Zbl 0588.58012

[27] S. Zhang, Doctoral Thesis, Nankai University, 1991.