caa a22 4500 388108908 CHVBK 20180307125347.0 cr unu---uuuuu 161130s1999 xx s 000 0 eng 10.1017/S0308210500030985 doi S0308210500030985 pii (NATIONALLICENCE)cambridge-10.1017/S0308210500030985 Genericity of the multibump dynamics for almost periodic Duffing-like systems [Elektronische Daten] 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. Copyright © Royal Society of Edinburgh 1999 Alessio Francesca Dipartimento di Matematica del Politecnico di Torino, Corso Duca degli Abruzzi, 24 - I 10129 Torino, Italy (alessio@dm.unito.it) Caldiroli Paolo Scuola Internazionale Superiore di Studi Avanzati, via Beirut, 2-4 - I 34013 Trieste, Italy (paolocal@sissa.it) Montecchiari Piero Dipartimento di Matematica dell'Università di Trieste, Piazzale Europa, 1 - I 34127 Trieste, Italy (montec@univ.trieste.it) Proceedings of the Royal Society of Edinburgh: Section A Mathematics Royal Society of Edinburgh Scotland Foundation 129/5(1999), 885-901 0308-2105 129:5<885 1999 129 PRM https://doi.org/10.1017/S0308210500030985 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S0308210500030985 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Alessio Francesca Dipartimento di Matematica del Politecnico di Torino, Corso Duca degli Abruzzi, 24 - I 10129 Torino, Italy (alessio@dm.unito.it) NATIONALLICENCE 700 1- Caldiroli Paolo Scuola Internazionale Superiore di Studi Avanzati, via Beirut, 2-4 - I 34013 Trieste, Italy (paolocal@sissa.it) NATIONALLICENCE 700 1- Montecchiari Piero Dipartimento di Matematica dell'Università di Trieste, Piazzale Europa, 1 - I 34127 Trieste, Italy (montec@univ.trieste.it) NATIONALLICENCE 773 0- Proceedings of the Royal Society of Edinburgh: Section A Mathematics Royal Society of Edinburgh Scotland Foundation 129/5(1999), 885-901 0308-2105 129:5<885 1999 129 PRM CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge