Heteroclinic motions joining almost periodic solutions for a class of Lagrangian systems

Francesca Alessio; Carlo Carminati; Piero Montecchiari

doi:10.3934/dcds.1999.5.569

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1999, Volume 5, Issue 3: 569-584. Doi: 10.3934/dcds.1999.5.569

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Heteroclinic motions joining almost periodic solutions for a class of Lagrangian systems

1.
Dipartimento di Matematica "R. Caccioppoli", Università di Napoli "Federico II" Via Cintia, I-80126 Napoli
2.
Dipartimento di Matematica, Università di Pisa, Via Buonarroti 2, I-56127 Pisa
3.
Dipartimento di Matematica, Università di Ancona, Via Brecce Bianche, I-60131 Ancona

Revised: February 28, 1999

Published: June 1999

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Abstract

We regard second order systems of the form $\ddot q = \nabla_qW(q, t), t\in \mathbb R, q \in \mathbb R^N,$ where $W(q, t)$ is $\mathbb Z^N$ periodic in $q$ and almost periodic in $t$. Variational arguments are used to prove the existence of heteroclinic solutions joining almost periodic solutions to the system.

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Mathematics Subject Classification: 34C37, 58Exx, 58Fxx.

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