manuscripta mathematica

, Volume 32, Issue 1–2, pp 149–189 | Cite as

Periodic solutions of asymptotically linear Hamiltonian systems

  • Herbert Amann
  • Eduard Zehnder


We prove existence and multiplicity results for periodic solutions of time dependent and time independent Hamiltonian equations, which are assumed to be asymptotically linear. The periodic solutions are found as critical points of a variational problem in a real Hilbert space. By means of a saddle point reduction this problem is reduced to the problem of finding critical points of a function defined on a finite dimensional subspace. The critical points are then found using generalized Morse theory and minimax arguments.


Hilbert Space Periodic Solution Saddle Point Number Theory Hamiltonian System 
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Copyright information

© Springer-Verlag 1980

Authors and Affiliations

  • Herbert Amann
    • 1
  • Eduard Zehnder
    • 2
  1. 1.Mathematisches Institut der Universität ZürichZürichSwitzerland
  2. 2.Mathematisches Institut der Ruhr-Universität BochumBochumGermany

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