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Index estimates for strongly indefinite functionals, periodic orbits and homoclinic solutions of first order Hamiltonian systems

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Abstract.

We improve Benci and Rabinowitz's Linking theorem for strongly indefinite functionals, giving estimates for a suitably defined relative Morse index of critical points. Such abstract result is applied to the existence problem of periodic orbits and homoclinic solutions of first order Hamiltonian systems in cases where the Palais-Smale condition does not hold.

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Authors and Affiliations

  1. Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa, Italy (e-mail: abbo@sns.it), , , , , , IT

    Alberto Abbondandolo

  2. Depto. de Ingeniería Matemática, Universidad de Concepción, Casilla 160-C, Concepción, Chile (e-mail: jmolina@ing-mat.udec.cl), , , , , , CL

    Juan Molina

Authors
  1. Alberto Abbondandolo
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  2. Juan Molina
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Received January 27, 1999 / Accepted January 14, 2000 / Published online July 20, 2000

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Abbondandolo, A., Molina, J. Index estimates for strongly indefinite functionals, periodic orbits and homoclinic solutions of first order Hamiltonian systems. Calc Var 11, 395–430 (2000). https://doi.org/10.1007/s005260000046

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  • DOI: https://doi.org/10.1007/s005260000046

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