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Periodic solutions of Birkhoff-Lewis type for the nonlinear wave equation

Pages: 102 - 109, Issue Special, September 2007

 Abstract        Full Text (214.5K)              

Luca Biasco - Dipartimento di Matematica, Università "Roma Tre", Largo S. L. Murialdo 1, 00146 Roma, Italy (email)
Laura Di Gregorio - Dipartimento di Matematica, Università “Roma Tre”, Largo S. L. Murialdo 1, 00146, Roma, Italy, United States (email)

Abstract: We prove the existence of infinitely many periodic solutions accumulating to zero for the one–dimensional nonlinear wave equation (vibrating string equation). The periods accumulate to zero and are both rational and irrational multiples of the string length.

Keywords:  Wave equation, periodic solutions, Nash–Moser IFT.
Mathematics Subject Classification:  Primary: 34C25, 35L05; Secondary: 37K50.

Received: September 2006;      Revised: January 2007;      Published: September 2007.