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Genericity of the multibump dynamics for almost periodic Duffing-like systems

Published online by Cambridge University Press:  14 November 2011

Francesca Alessio ,
Paolo Caldiroli  and
Piero Montecchiari
Francesca Alessio
Affiliation:
Dipartimento di Matematica del Politecnico di Torino, Corso Duca degli Abruzzi, 24 – I 10129 Torino, Italy (alessio@dm.unito.it)
Paolo Caldiroli
Affiliation:
Scuola Internazionale Superiore di Studi Avanzati, via Beirut, 2-4 – I 34013 Trieste, Italy (paolocal@sissa.it)
Piero Montecchiari
Affiliation:
Dipartimento di Matematica dell'Università di Trieste, Piazzale Europa, 1 – I 34127 Trieste, Italy (montec@univ.trieste.it)
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Abstract

In this paper we consider ‘slowly’ oscillating perturbations of almost periodic Duffing-like systems, i.e. systems of the form ü = u − (a(t) + α(wt))W′(u), t ∈ ℝ, u ∈ ℝN, where W ∈ C2N(ℝN, ℝ) is superquadratic and a and α are positive and almost periodic. By variational methods, we prove that if w > 0 is small enough, then the system admits a multibump dynamics. As a consequence we get that the system ü = u − a(t)W′(u), t ∈ ℝ, u ∈ ℝN, admits multibump solutions whenever a belongs to an open dense subset of the set of positive almost periodic continuous functions.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 129 , Issue 5 , 1999 , pp. 885 - 901
Copyright
Copyright © Royal Society of Edinburgh 1999

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