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manuscripta mathematica

, Volume 59, Issue 4, pp 441–456 | Cite as

A “Birkhoff-Lewis” type result for a class of Hamiltonian systems

  • Vieri Benci
  • Donato Fortunato
Article

Abstract

This paper contains results concerning the existence of long periodic solutions of nonautonomous Hamiltonian systems near the origin.

Keywords

Periodic Solution Number Theory Hamiltonian System Algebraic Geometry Topological Group 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    - ARNOLD,V.I.: Mathematical Methods of Classical Mechanics. Berlin-Heidelberg-New York; Springer-Verlag 1978Google Scholar
  2. [2]
    - BENCI,V.-CAPOZZI,A.-FORTUNATO,D.: Periodic solutions of Hamilt onian systems with superquadratic potential, Ann.Mat.Pura Appl.143, 1–46, (1986)Google Scholar
  3. [3]
    - BENCI,V. -RABINOWITZ,P.H.: Critical point theorems for indefinite functionals. Inv.Math.52, 336–352, (1979)Google Scholar
  4. [4]
    - BIRKHOFF,G.D.-LEWIS,D.C.: On the periodic motions near a given periodic motion of a dynamical system. Ann.Mat.Pura Appl.12, 117–133, (1933)Google Scholar
  5. [5]
    - GELFAND,I.-LIDSKY,V.: On the structure of regions of stability of linear canonical systems of differential equations with periodic coefficients, Uspekhi Mat.Naouk,10, (1955), 3–40 (A.M.S.Translation,8, 143–181, (1958))Google Scholar
  6. [6]
    - HARRIS,T.C.: Periodic solutions of arbitrarily long periods in Hamiltonian systems. J.Diff.Eq.4, 131–141, (1968)Google Scholar
  7. [7]
    - JÖRGENS, K. -WEIDMANN, J.: Spectral properties of Hamiltonian operators. Berlin-Heidelberg-New York; Springer-Verlag lecture notes in Math., (1973)Google Scholar
  8. [8]
    - KREIN,M.: Generalization of certain investigations of A.H.Liapounov on linear differential equations with periodic coefficients. Doklady Akad.Naouk, USSR,73, 445–448, (1950)Google Scholar
  9. [9]
    - MOSER, J.: Proof of a generalized form of a fixed point theorem due to G.D.Birkhoff. Berlin-Heidelberg-New York: Springer-Verlag lecture notes in Math.,597, 464–494, (1977)Google Scholar
  10. [10]
    - RABINOWITZ,P.H.: On Subharmonic solutions of Hamiltonian systems. Comm.Pure Appl.Math.,33, 609–633, (1980)Google Scholar
  11. [11]
    - RABINOWITZ,P.H.: Minimax Methods in Critical point Theory with applications to differential equations. Conference series in Mathematics, A.M.S.,65, (1986)Google Scholar
  12. [l2]
    - TARANTELLO,G.: Subharmonic solutions for Hamiltonian systems via aZ p pseudoindex theory, preprintGoogle Scholar

Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • Vieri Benci
    • 1
  • Donato Fortunato
    • 2
  1. 1.Istituto di Matematiche Applicate-UniversitàPisaItaly
  2. 2.Dipartimento di Matematica UniversitàBariItaly

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