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Genericity of the multibump dynamics for almost periodic Duffing-like systems
Published online by Cambridge University Press: 14 November 2011
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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