Displaying similar documents to “Nonlinear vibrations of completely resonant wave equations”

Quasi-periodic oscillations for wave equations under periodic forcing

Massimiliano Berti, Michela Procesi (2005)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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Existence of quasi-periodic solutions with two frequencies of completely resonant, periodically forced, nonlinear wave equations with periodic spatial boundary conditions is established. We consider both the cases the forcing frequency is (Case A) a rational number and (Case B) an irrational number.

Bifurcation of free vibrations for completely resonant wave equations

Massimiliano Berti, Philippe Bolle (2004)

Bollettino dell'Unione Matematica Italiana

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We prove existence of small amplitude, 2p/v-periodic in time solutions of completely resonant nonlinear wave equations with Dirichlet boundary conditions for any frequency ω belonging to a Cantor-like set of positive measure and for a generic set of nonlinearities. The proof relies on a suitable Lyapunov-Schmidt decomposition and a variant of the Nash-Moser Implicit Function Theorem.

Periodic solutions of nonlinear wave equations with non-monotone forcing terms

Massimiliano Berti, Luca Biasco (2005)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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Existence and regularity of periodic solutions of nonlinear, completely resonant, forced wave equations is proved for a large class of non-monotone forcing terms. Our approach is based on a variational Lyapunov-Schmidt reduction. The corresponding infinite dimensional bifurcation equation exhibits an intrinsic lack of compactness. This difficulty is overcome finding a-priori estimates for the constrained minimizers of the reduced action functional, through techniques inspired by regularity...