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July  1997, 3(3): 401-418. doi: 10.3934/dcds.1997.3.401

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

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

Received  December 1996 Published  April 1997

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.
Citation: Paolo Perfetti. An infinite-dimensional extension of a Poincaré's result concerning the continuation of periodic orbits. Discrete and Continuous Dynamical Systems, 1997, 3 (3) : 401-418. doi: 10.3934/dcds.1997.3.401
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