Lindstedt series for periodic solutions of beam equations with quadratic and velocity dependent nonlinearities

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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.
29 pages 6 figures

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Functional Analysis, Analysis of PDEs, 35B10 (primary), 35B32, 35L70, 47H15 (secondary)

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http://salesiana.dossiersoluciones.com/handle/123456789/75188

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0505283
 http://arxiv.org/abs/math/0505283

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arXiv