Geodesic
Soluzioni periodiche di PDEs Hamiltoniane
Bollettino della Unione matematica italiana, Série 8, 7B (2004) no. 3, pp. 647-661.

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Presentiamo nuovi risultati di esistenza e molteplicità di soluzioni periodiche di piccola ampiezza per equazioni alle derivate parziali Hamiltoniane. Otteniamo soluzioni periodiche di equazioni «completamente risonanti» aventi nonlinearità generali grazie ad una riduzione di tipo Lyapunov-Schmidt variazionale ed usando argomenti di min-max. Per equazioni «non risonanti» dimostriamo l'esistenza di soluzioni periodiche di tipo Birkhoff-Lewis, mediante un'opportuna forma normale di Birkhoff e realizzando nuovamente una riduzione di tipo Lyapunov-Schmidt.
New existence and multiplicity results of small amplitude periodic solutions for nonlinear Hamiltonian PDEs are presented. We obtain periodic solutions of «completely resonant» equations with any general nonlinearity thanks to a Lyapunov-Schmidt reduction, variational in nature, and min-max topological arguments. For «non resonant» equations we prove existence of periodic solutions of Birkhoff-Lewis type, by means of a suitable Birkhoff normal form and implementing again a Lyapunov-Schmidt variational reduction. 
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Berti, Massimiliano. Soluzioni periodiche di PDEs Hamiltoniane. Bollettino della Unione matematica italiana, Série 8, 7B (2004) no. 3, pp. 647-661. http://geodesic.mathdoc.fr/item/BUMI_2004_8_7B_3_a6/

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