We study the existence of periodic solutions for the infinite-dimensional second order system $\ddot x=V_{x},\ x\in{\Bbb T}^{{\Bbb Z}_+}.$ Using the Implicit-Function-Theorem, we prove the existence of time-periodic solutions at \lq\lq high frequencies"; no \lq\lq smallness condition" on $V(x)$ is required.
Perfetti, P. (1997). An infinite-dimensional extension of a Poincar\'e's result concerning the continuation of periodic orbits. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 3(3), 401-418.
An infinite-dimensional extension of a Poincar\'e's result concerning the continuation of periodic orbits
PERFETTI, PAOLO
1997-07-01
Abstract
We study the existence of periodic solutions for the infinite-dimensional second order system $\ddot x=V_{x},\ x\in{\Bbb T}^{{\Bbb Z}_+}.$ Using the Implicit-Function-Theorem, we prove the existence of time-periodic solutions at \lq\lq high frequencies"; no \lq\lq smallness condition" on $V(x)$ is required.File in questo prodotto:
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