Some perturbation results for non-linear problems

Carlo Carminati

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1993)

  • Volume: 4, Issue: 4, page 243-250
  • ISSN: 1120-6330

Abstract

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We discuss the existence of closed geodesic on a Riemannian manifold and the existence of periodic solution of second order Hamiltonian systems.

How to cite

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Carminati, Carlo. "Some perturbation results for non-linear problems." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 4.4 (1993): 243-250. <http://eudml.org/doc/244265>.

@article{Carminati1993,
abstract = {We discuss the existence of closed geodesic on a Riemannian manifold and the existence of periodic solution of second order Hamiltonian systems.},
author = {Carminati, Carlo},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Critical point theory; Closed geodesies; Second order Hamiltonian systems; periodic solutions; geodesics},
language = {eng},
month = {12},
number = {4},
pages = {243-250},
publisher = {Accademia Nazionale dei Lincei},
title = {Some perturbation results for non-linear problems},
url = {http://eudml.org/doc/244265},
volume = {4},
year = {1993},
}

TY - JOUR
AU - Carminati, Carlo
TI - Some perturbation results for non-linear problems
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1993/12//
PB - Accademia Nazionale dei Lincei
VL - 4
IS - 4
SP - 243
EP - 250
AB - We discuss the existence of closed geodesic on a Riemannian manifold and the existence of periodic solution of second order Hamiltonian systems.
LA - eng
KW - Critical point theory; Closed geodesies; Second order Hamiltonian systems; periodic solutions; geodesics
UR - http://eudml.org/doc/244265
ER -

References

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  1. ALBER, S. I., On periodicity problems in the calculus of variations in the large. Amer. Math. Soc. Transl., (2), 14, 1960. Zbl0094.08202MR113234
  2. AMBROSETTI, A., Critical points and non-linear variational problems. Supplément Bull. Soc. Math, de France, n. 49, 120, 1992. Zbl0766.49006
  3. AMBROSETTI, A. - BENCI, V. - LONG, Y., A note on the existence of multiple brake orbits. J.N.A.-T.M.A., to appear. Zbl0811.70015
  4. AMBROSETTI, A. - COTI ZELATI, V. - EKELAND, I., Symmetry breaking in Hamiltonian systems. J. Diff. Equat., 67, 1987, 165-184. Zbl0606.58043MR879691DOI10.1016/0022-0396(87)90144-6
  5. BENCI, V. - GIANNONI, F., A New Proof of the Existence of a Brake Orbit. Advanced Topics in the Theory of Dynamical Systems, Academic Press, New York1990. Zbl0674.34034MR996075
  6. EKELAND, I. - LASRY, J. M., On the number of periodic trajectories for a Hamiltonian flow on a convex energy surface. Ann. of Math., 112, 1980, 283-319. Zbl0449.70014MR592293DOI10.2307/1971148
  7. KLINGENBERG, W., Lectures on Closed Geodesics. Springer, 1978. Zbl0397.58018MR478069
  8. SCHWARTZ, J. T., Nonlinear functional Analysis. Gordon & Breach, New York1969. Zbl0203.14501MR433481
  9. STRUWE, M., Variational Methods. Springer, 1990. Zbl0746.49010MR1078018
  10. SZULKIN, A., An index theory and existence of multiple brake orbits for star-shaped hamiltonian systems. Math. Ann., 283, 1989, 241-255. Zbl0642.58030MR980596DOI10.1007/BF01446433

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