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.
@article{BUMI_2004_8_7B_2_a16,
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/}
}
TY - JOUR AU - Berti, Massimiliano AU - Bolle, Philippe TI - Bifurcation of free vibrations for completely resonant wave equations JO - Bollettino della Unione matematica italiana PY - 2004 SP - 519 EP - 528 VL - 7B IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/BUMI_2004_8_7B_2_a16/ LA - en ID - BUMI_2004_8_7B_2_a16 ER -
%0 Journal Article %A Berti, Massimiliano %A Bolle, Philippe %T Bifurcation of free vibrations for completely resonant wave equations %J Bollettino della Unione matematica italiana %D 2004 %P 519-528 %V 7B %N 2 %I mathdoc %U http://geodesic.mathdoc.fr/item/BUMI_2004_8_7B_2_a16/ %G en %F BUMI_2004_8_7B_2_a16
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/