Soluzioni periodiche di PDEs Hamiltoniane

Massimiliano Berti

Bollettino dell'Unione Matematica Italiana (2004)

  • Volume: 7-B, Issue: 3, page 647-661
  • ISSN: 0392-4041

Abstract

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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.

How to cite

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Berti, Massimiliano. "Soluzioni periodiche di PDEs Hamiltoniane." Bollettino dell'Unione Matematica Italiana 7-B.3 (2004): 647-661. <http://eudml.org/doc/195679>.

@article{Berti2004,
abstract = {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.},
author = {Berti, Massimiliano},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {ita},
month = {10},
number = {3},
pages = {647-661},
publisher = {Unione Matematica Italiana},
title = {Soluzioni periodiche di PDEs Hamiltoniane},
url = {http://eudml.org/doc/195679},
volume = {7-B},
year = {2004},
}

TY - JOUR
AU - Berti, Massimiliano
TI - Soluzioni periodiche di PDEs Hamiltoniane
JO - Bollettino dell'Unione Matematica Italiana
DA - 2004/10//
PB - Unione Matematica Italiana
VL - 7-B
IS - 3
SP - 647
EP - 661
AB - 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.
LA - ita
UR - http://eudml.org/doc/195679
ER -

References

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