Bifurcation of free vibrations for completely resonant wave equations
Berti, Massimiliano ; Bolle, Philippe
Bollettino dell'Unione Matematica Italiana, Tome 7-A (2004), p. 519-528 / Harvested from Biblioteca Digitale Italiana di Matematica
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We prove existence of small amplitude, 2p/v-periodic in time solutions of completely resonant nonlinear wave equations with Dirichlet boundary conditions for any frequency ω belonging to a Cantor-like set of positive measure and for a generic set of nonlinearities. The proof relies on a suitable Lyapunov-Schmidt decomposition and a variant of the Nash-Moser Implicit Function Theorem.

Dimostriamo l'esistenza di soluzioni di piccola ampiezza, 2⁢π/ω-periodiche nel tempo, per equazioni delle onde nonlineari completamente risonanti, per frequenze ω in un insieme di Cantor di misura positiva e per un insieme generico di nonlinearità. La dimostrazione si basa su una opportuna decomposizione di Lyapunov-Schmidt e su una variante dei teoremi di funzione implicita alla Nash-Moser.

Publié le : 2004-06-01
@article{BUMI_2004_8_7B_2_519_0,
     author = {Massimiliano Berti and Philippe Bolle},
     title = {Bifurcation of free vibrations for completely resonant wave equations},
     journal = {Bollettino dell'Unione Matematica Italiana},
     volume = {7-A},
     year = {2004},
     pages = {519-528},
     zbl = {1182.35166},
     mrnumber = {2072952},
     language = {en},
     url = {http://dml.mathdoc.fr/item/BUMI_2004_8_7B_2_519_0}
}

Berti, Massimiliano; Bolle, Philippe. Bifurcation of free vibrations for completely resonant wave equations. Bollettino dell'Unione Matematica Italiana, Tome 7-A (2004) pp. 519-528. http://gdmltest.u-ga.fr/item/BUMI_2004_8_7B_2_519_0/

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