Periodic bounce trajectories with a low number of bounce points
Benci, V. ; Giannoni, F.
Annales de l'I.H.P. Analyse non linéaire, Tome S6 (1989), p. 73-93 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU)
Publié le : 1989-01-01
@article{AIHPC_1989__6_1_73_0,
     author = {Benci, Vieri and Giannoni, Fabio},
     title = {Periodic bounce trajectories with a low number of bounce points},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {S6},
     year = {1989},
     pages = {73-93},
     mrnumber = {984148},
     zbl = {0667.34054},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_1989__6_1_73_0}
}

Benci, V.; Giannoni, F. Periodic bounce trajectories with a low number of bounce points. Annales de l'I.H.P. Analyse non linéaire, Tome S6 (1989) pp. 73-93. http://gdmltest.u-ga.fr/item/AIHPC_1989__6_1_73_0/

[1] P. Bartolo, V. Benci and D. Fortunato, Abstract Critical Point Theorems and Application to Some Nonlinear Problems with Strong Resonance at Infinity, Nonlin. Anal. T.M.A., Vol. 7, 1983, pp. 981-1012. | MR 713209 | Zbl 0522.58012

[2] V. Benci, Normal Modes of a Lagrangian System Constrained in a Potential Well, Ann. Inst. H. Poincaré, Vol. 1, 1984, pp. 379-400. | Numdam | MR 779875 | Zbl 0561.58006

[3] V. Benci ,A New Approach to the Morse-Conley Index Theory, Proceed. on "Recent Advances in Hamiltonian Systems", Dell'Antonio and D'Onofrio Ed., World Scientific Publ., 1987. | MR 902622 | Zbl 0665.58007

[4] V.. Benci, Some Applications of the Generalized Morse-Conley Index, Conf. Sem. Mat. Univ. Bari, Vol. 218, 1987, pp. 1-31. | MR 898735 | Zbl 0656.58006

[5] V. Benci, A New Approach to the Morse-Conley Index Theory and Some Applications, to appear on Ann. Mat. Pure Appl. | Zbl 0778.58011

[6] W.. Bos, Kritische Schnen auf Riemannschen Elementarraumstücken, Math. Ann., Vol. 151, 1983, pp. 431-451. | MR 159297 | Zbl 0113.15204

[7] G. Buttazzo and D. Percivale, Sull'approssimazione del rimbalzo unidimensionale, Ric. Mat., Vol. 30, 1981, pp. 217-231. | MR 682529 | Zbl 0508.73024

[8] G. Buttazzo and D. Percivale, On the Approximation of the Elastic Bounce Problem on Riemanian Manifolds, Journ. Diff. Eq., 47, 1983, pp. 227-245. | MR 688104 | Zbl 0498.58011

[9] M. Carriero and E. Pascali, Il problema del rimbalzo unidimensionale e sue penalizzazioni non convesse, Rend. Mat., Vol. 13, 1980, pp. 541-553. | MR 615514 | Zbl 0461.73049

[10] M. Carriero, A. Leaci and E. Pascali, Convergenza per l'equazione degli integrali primi associati al problema del rimbalzo unidimensionale, Ann. Mat. Pura Appl., Vol. 133, 1983, pp. 227-256. | MR 725027 | Zbl 0545.73014

[11] M. Degiovanni, Multiplicity of Solutions for the Bounce Problem. Journ. Diff. Eq., Vol. 54, 1984, pp. 414-428. | MR 760380 | Zbl 0505.34006

[12] F. Giannoni, Periodic Bounce Solutions of Dynamical Conservative Systems and their Minimal Period, to appear on Nonlin. Anal. T.M.A. | MR 1036212 | Zbl 0702.34036

[13] H. Gluck and W. Ziller, Existence of Peridoic Motions of Conservative Systems, Seminar on Minimal Submanifolds, Bombieri Ed., Princeton University Press, 1983. | MR 795229 | Zbl 0546.58040

[14] R. Peirone, Bounce Trajectories in Plane Tubolar Domains (to appear). | MR 1142435 | Zbl 0741.58021

[15] D. Percivale, Uniqueness in Elastic Bounce Problem, Journ. Diff. Eq., Vol. 56, 1985, pp. 206-215. | MR 774163 | Zbl 0521.73006

[16] L. Penrose and R. Penrose, Puzzles for Christmas, The New Scientist, 1580-81 and 1597, 25 Dec. 1958.

[17] P.H. Rabinowitz, Minimax Methods in Critical Point Theory with Applications to Differential Equations, Reg. Conf. Ser., Amer. Math. Soc., 65, 1986. | MR 845785 | Zbl 0609.58002

[18] J. Rauch, Illumination of Bounded Domains, Amer. Math. Month., 85, 1978, pp. 359- 361. | MR 482537 | Zbl 0399.52006