Skip to main content
Log in

Periodic motions of conservative systems with singular potentials

  • Published:
Nonlinear Differential Equations and Applications NoDEA Aims and scope Submit manuscript

Abstract

The existence of closed orbits with prescribed energy for second order Hamiltonian Systems with singular potentials is studied.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. A. AMBROSETTI, Critical points and nonlinear variational problems,Bull. Soc. Math. France 120 (1992), no. 49, Cours de la chaire Lagrange

  2. A. AMBROSETTI, V. COTI ZELATI, Closed orbits of fixed energy for singular Hamiltonian systems,Arch. Rat. Mech. and Anal.,112, 339–362 (1990)

    Google Scholar 

  3. A. AMBROSETTI, V. COTI ZELATI, Closed orbits of fixed energy for a class ofn-body problems,Ann. Inst. H. Poincaré, Anal. Non Linéaire 9, 187–200 (1992), Addendum,Ann. Inst. H. Poincaré, Anal. Non Linéaire 9, 337–338 (1992)

    Google Scholar 

  4. A. AMBROSETTI, V. COTI ZELATI,Lagrangian Systems with Singular Potentials, Birkhäuser, Basel, to appear

  5. A. BAHRI, P.H. RABINOWITZ, A minimax method for a class of Hamiltonian systems with singular potential,J. Funct. Anal. 82, 412–428 (1989)

    Google Scholar 

  6. V. BENCI, Closed geodesics for the Jacobi metric and periodic solutions of prescribed energy of natural Hamiltonian systems,Ann. Inst. H. Poincaré: Anal. Non Linéaire 3, 401–412 (1984)

    Google Scholar 

  7. V. BENCI, D. FORTUNATO, Subharmonic solutions of prescribed minimal period for non-autonomous differential equations, in:Recent advances in Hamiltonian systems (G.F. Dell'Antonio and B.D'Onofrio, eds.), World Scientific, 1987, pag. 83–96

  8. V. BENCI, F. GIANNONI, A new proof of the existence of a brake oribt,Advanced Topics in the Theory of Dynamical Systems, Academic Press, New York, 1990

    Google Scholar 

  9. V. BENCI, P.H. RABINOWITZ, Critical point theorems for indefinite functionals,Invent. Math. 52, 241–273 (1979)

    Google Scholar 

  10. S.V. BOLOTIN: Libration motions of natural dynamical systems,Moscow Univ. Math. Bull. 33-5/6, 49–53 (1978)

    Google Scholar 

  11. H. GLUCK, W. ZILLER, Existence of periodic motions of conservative systems,Seminar on minimal submanifolds, Princeton University Press, 1986, pag. 155–161

  12. K. HAYASHI, Periodic solutions of classical Hamiltonian systems,Tokyo J. Math. 6, 473–486 (1983)

    Google Scholar 

  13. H. HOFER, E. ZEHNDER, Periodic solutions on hypersurfaces and a result by C. Viterbo,Invent. Math. 90, 1–9 (1987)

    Google Scholar 

  14. A.C. LAZER, S. SOLIMINI, Nontrivial solutions of operator equations and Morse indices of critical points of min-max type,Nonlinear Analysis: T.M.A. 12, 761–775 (1988)

    Google Scholar 

  15. P.H. RABINOWITZ, Periodic solutions of a Hamiltonian system on a prescribed energy surface,J. Diff. Eq. 33, 336–352 (1979)

    Google Scholar 

  16. P.H. RABINOWITZ, A note on periodic solutions of prescribed energy for singular Hamiltonian systems, preprint (1992)

  17. H. SEIFERT, Periodische Bewegungen mechanischer Systeme,Math. Z. 51, 197–216 (1948)

    Google Scholar 

  18. M. STRUWE, Existence of Hamiltonian systems on almost every energy surfaces,Bol. Soc. Brasil. Mat. (1979)

  19. K. TANAKA, A prescribed energy problem for a singular Hamiltonian system with a weak force,J. Funct. Anal., (to appear)

  20. C. VITERBO, A proof of Weinstein's conjecture inR 2n,Ann. Inst. H. Poincaré: Anal. Non Linéaire 4, 337–356 (1987)

    Google Scholar 

  21. C. VITERBO, Indice de Morse des points critiques obtenus par minimax,Ann. Inst. H. Poincaré, Anal. Non Linéaire 5, 221–225 (1988)

    Google Scholar 

  22. A. WEINSTEIN, Periodic orbits for convex Hamiltonian systems,Ann. of Math. (2)108, 507–518 (1978)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

The first author was supported by M.U.R.S.T.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ambrosetti, A., Struwe, M. Periodic motions of conservative systems with singular potentials. NoDEA 1, 179–202 (1994). https://doi.org/10.1007/BF01193951

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01193951

Keywords

Navigation