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. 
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     author = {Berti, Massimiliano and Bolle, Philippe},
     title = {Bifurcation of free vibrations for completely resonant wave equations},
     journal = {Bollettino della Unione matematica italiana},
     pages = {519--528},
     publisher = {mathdoc},
     volume = {Ser. 8, 7B},
     number = {2},
     year = {2004},
     zbl = {1182.35166},
     mrnumber = {MR2072952},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BUMI_2004_8_7B_2_a16/}
}
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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/