Cantor families of periodic solutions for completely resonant nonlinear wave equations
| dc.creator | Berti, M. | |
| dc.creator | Bolle, P. | |
| dc.date | 2004-10-29 | |
| dc.date.accessioned | 2026-07-07T05:13:47Z | |
| dc.date.available | 2026-07-07T05:13:47Z | |
| dc.description | We prove existence of small amplitude, $2π\slash \om$-periodic in time solutions of completely resonant nonlinear wave equations with Dirichlet boundary conditions, for any frequency $ \om $ belonging to a Cantor-like set of positive measure and for a new set of nonlinearities. The proof relies on a suitable Lyapunov-Schmidt decomposition and a variant of the Nash-Moser Implicit Function Theorem. In spite of the complete resonance of the equation we show that we can still reduce the problem to a {\it finite} dimensional bifurcation equation. Moreover, a new simple approach for the inversion of the linearized operators required by the Nash-Moser scheme is developed. It allows to deal also with nonlinearities which are not odd and with finite spatial regularity. | |
| dc.identifier | https://arxiv.org/abs/math/0410618 | |
| dc.identifier | http://arxiv.org/abs/math/0410618 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/73043 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 35L05, 37K50, 58E05 | |
| dc.title | Cantor families of periodic solutions for completely resonant nonlinear wave equations | |
| dc.type | text |