Lindstedt series for periodic solutions of beam equations with quadratic and velocity dependent nonlinearities
| dc.creator | Mastropietro, Vieri | |
| dc.creator | Procesi, Michela | |
| dc.date | 2005-05-13 | |
| dc.date.accessioned | 2026-07-07T05:19:53Z | |
| dc.date.available | 2026-07-07T05:19:53Z | |
| dc.description | We prove the existence of small amplitude periodic solutions, for a large Lebesgue measure set of frequencies, in the nonlinear beam equation with a weak quadratic and velocity dependent nonlinearity and with Dirichlet boundary conditions. Such nonlinear PDE can be regarded as a simple model describing oscillations of flexible structures like suspension bridges in presence of an uniform wind flow. The periodic solutions are explicitly constructed by means of a perturbative expansion which can be considered the analogue of the Lindstedt series expansion for the invariant tori in classical mechanics. The periodic solutions are not analytic but defined only in a Cantor set, and resummation techniques of divergent powers series are used in order to control the small divisors problem. | |
| dc.description | 29 pages 6 figures | |
| dc.identifier | https://arxiv.org/abs/math/0505283 | |
| dc.identifier | http://arxiv.org/abs/math/0505283 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/75188 | |
| dc.subject | Functional Analysis | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 35B10 (primary), 35B32, 35L70, 47H15 (secondary) | |
| dc.title | Lindstedt series for periodic solutions of beam equations with quadratic and velocity dependent nonlinearities | |
| dc.type | text |