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We consider the Kirchhoff equation for a vibrating body, in any dimension, in the presence of a time-periodic external forcing with period and amplitude . We treat both Dirichlet and space-periodic boundary conditions, and both analytic and Sobolev regularity. We prove the existence, regularity and local uniqueness of time-periodic solutions, using a Nash-Moser iteration scheme. The results hold for parameters in a Cantor set with asymptotically full measure as .
@article{ASNSP_2009_5_8_1_117_0,
author = {Baldi, Pietro},
title = {Periodic solutions of forced {Kirchhoff} equations},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
pages = {117--141},
publisher = {Scuola Normale Superiore, Pisa},
volume = {Ser. 5, 8},
number = {1},
year = {2009},
mrnumber = {2512203},
zbl = {1180.35040},
language = {en},
url = {http://geodesic.mathdoc.fr/item/ASNSP_2009_5_8_1_117_0/}
}
TY - JOUR AU - Baldi, Pietro TI - Periodic solutions of forced Kirchhoff equations JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2009 SP - 117 EP - 141 VL - 8 IS - 1 PB - Scuola Normale Superiore, Pisa UR - http://geodesic.mathdoc.fr/item/ASNSP_2009_5_8_1_117_0/ LA - en ID - ASNSP_2009_5_8_1_117_0 ER -
%0 Journal Article %A Baldi, Pietro %T Periodic solutions of forced Kirchhoff equations %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2009 %P 117-141 %V 8 %N 1 %I Scuola Normale Superiore, Pisa %U http://geodesic.mathdoc.fr/item/ASNSP_2009_5_8_1_117_0/ %G en %F ASNSP_2009_5_8_1_117_0
Baldi, Pietro. Periodic solutions of forced Kirchhoff equations. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 8 (2009) no. 1, pp. 117-141. http://geodesic.mathdoc.fr/item/ASNSP_2009_5_8_1_117_0/