An infinite-dimensional extension of a Poincar&eacute;'s result concerning the continuation of periodic orbits

Paolo Perfetti

doi:10.3934/dcds.1997.3.401

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1997, Volume 3, Issue 3: 401-418. Doi: 10.3934/dcds.1997.3.401

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An infinite-dimensional extension of a Poincaré's result concerning the continuation of periodic orbits

Paolo Perfetti^1,

1.
Dipartimento di matematica II Università di Roma, via della Ricerca Scientifica 00133 Roma

Received: December 1996

Published: July 1997

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Abstract

We study the existence of periodic solutions for the infinite-dimensional second order system $\ddot x=V_{x},\ x\in\mathbb{T}^{\mathbb{Z}_+}.$ Using the Implicit-Function-Theorem, we prove the existence of time-periodic solutions at "high frequencies"; no "smallness condition" on $V(x)$ is required.

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Mathematics Subject Classification: 26B10, 34A15, 34C15.

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