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.

We consider the Kirchhoff equation for a vibrating body, in any dimension, in the presence of a time-periodic external forcing with period $2\pi /\omega$ and amplitude $\epsilon$. 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 $\left(\omega ,\epsilon \right)$ in a Cantor set with asymptotically full measure as $\epsilon \to 0$.

Classification: 35L70,  45K05,  35B10,  37K55
Baldi, Pietro 1

1 Dipartimento di Matematica e Applicazioni, “R. Caccioppoli”, Università degli Studi di Napoli, “Federico II”, Via Cintia, Monte S. Angelo, 80126 Napoli, Italia
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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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