KAM techniques in PDE
Ricardo Pérez-Marco (2001-2002)
Séminaire Bourbaki
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Ricardo Pérez-Marco (2001-2002)
Séminaire Bourbaki
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Massimiliano Berti, Michela Procesi (2005)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
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Existence of quasi-periodic solutions with two frequencies of completely resonant, periodically forced, nonlinear wave equations with periodic spatial boundary conditions is established. We consider both the cases the forcing frequency is (Case A) a rational number and (Case B) an irrational number.
Wei-Min Wang (2004-2005)
Séminaire Équations aux dérivées partielles
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Giorgilli, Antonio, Locatelli, Ugo (1997)
Mathematical Physics Electronic Journal [electronic only]
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Eliasson, L.H. (1996)
Mathematical Physics Electronic Journal [electronic only]
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A. Salvatore (1985)
Rendiconti del Seminario Matematico della Università di Padova
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Massimiliano Berti (2007)
Banach Center Publications
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We present recent existence results of small amplitude periodic and quasi-periodic solutions of completely resonant nonlinear wave equations. Both infinite-dimensional bifurcation phenomena and small divisors difficulties occur. The proofs rely on bifurcation theory, Nash-Moser implicit function theorems, dynamical systems techniques and variational methods.
H. Beirão da Veiga (1990)
Rendiconti del Seminario Matematico della Università di Padova
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H. Amann, E. Zehnder (1980)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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