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

Luca Biasco; Laura Di Gregorio

doi:10.3934/proc.2007.2007.102

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2007, Volume 2007: 102-109. Doi: 10.3934/proc.2007.2007.102 open access

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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

Received: August 31, 2006

Revised: December 31, 2006

Published: August 2007

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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.

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Mathematics Subject Classification: Primary: 34C25, 35L05; Secondary: 37K50.

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