Geodesic
Bifurcation of free vibrations for completely resonant wave equations
Bollettino della Unione matematica italiana, Série 8, 7B (2004) no. 2, pp. 519-528.

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

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 $\omega$ 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, $2\pi/\omega$-periodiche nel tempo, per equazioni delle onde nonlineari completamente risonanti, per frequenze $\omega$ 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. 
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     title = {Bifurcation of free vibrations for completely resonant wave equations},
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Berti, Massimiliano; Bolle, Philippe. Bifurcation of free vibrations for completely resonant wave equations. Bollettino della Unione matematica italiana, Série 8, 7B (2004) no. 2, pp. 519-528. http://geodesic.mathdoc.fr/item/BUMI_2004_8_7B_2_a16/

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