Periodic solutions of forced Kirchhoff equations
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 8 (2009) no. 1, p. 117-141

We consider the Kirchhoff equation for a vibrating body, in any dimension, in the presence of a time-periodic external forcing with period 2π/ω and amplitude ε. 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 (ω,ε) in a Cantor set with asymptotically full measure as ε0.

Classification:  35L70,  45K05,  35B10,  37K55
@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},
     publisher = {Scuola Normale Superiore, Pisa},
     volume = {Ser. 5, 8},
     number = {1},
     year = {2009},
     pages = {117-141},
     zbl = {1180.35040},
     mrnumber = {2512203},
     language = {en},
     url = {http://www.numdam.org/item/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, Serie 5, Volume 8 (2009) no. 1, pp. 117-141. http://www.numdam.org/item/ASNSP_2009_5_8_1_117_0/

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