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2007, 2007(Special): 102-109. doi: 10.3934/proc.2007.2007.102

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

Luca Biasco 1, and  Laura Di Gregorio 2,

1. 

Dipartimento di Matematica, Università "Roma Tre", Largo S. L. Murialdo 1, 00146 Roma
2. 

Dipartimento di Matematica, Università “Roma Tre”, Largo S. L. Murialdo 1, 00146, Roma, Italy, United States

Received  September 2006 Revised  January 2007 Published  September 2007

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: 37K5.
Citation: Luca Biasco, Laura Di Gregorio. Periodic solutions of Birkhoff-Lewis type for the nonlinear wave equation. Conference Publications, 2007, 2007 (Special) : 102-109. doi: 10.3934/proc.2007.2007.102
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