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Galerkin’s method, monotonicity and linking for indefinite Hamiltonian systems with bounded potential energy

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Abstract.

A combination of Galerkin’s method and linking theory with monotonicity in the calculus of variations is used to study Hamiltonian systems in which the kinetic-energy functional is a (not necessarily definite) quadratic form and the potential-energy functional may be bounded. The existence of non-constant brake periodic orbits for almost all prescribed energies is established. An example of a Hamiltonian system which satisfies our hypotheses but has no non-constant brake periodic orbits with energy in an uncountable set of measure zero is given. Additional hypotheses, sufficient to ensure the existence of non-constant brake periodic orbits of all energies, are found.

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Authors and Affiliations

  1. Department of Mathematical Sciences, University of Bath, BA2 7AY, Bath, UK

    D. J. Crispin & J. F. Toland

Authors
  1. D. J. Crispin
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  2. J. F. Toland
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Received: 28 November 2003, Accepted: 2 June 2004, Published online: 3 September 2004

Mathematics Subject Classification (2000):

37J45

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Crispin, D.J., Toland, J.F. Galerkin’s method, monotonicity and linking for indefinite Hamiltonian systems with bounded potential energy. Calc. Var. 23, 205–226 (2005). https://doi.org/10.1007/s00526-004-0297-2

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  • DOI: https://doi.org/10.1007/s00526-004-0297-2

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