In this paper we consider "slowly" oscillating perturbations of almost periodic Duffing-like systems, i.e., systems of the form $\ddot u=u-(a(t)+\alpha(\omega t))W'(u)$, $t\in\mathbb{R}$, $u\in\mathbb{R}^N$ where $W\in C^{2N}(\mathbb{R}^N,\mathbb{R})$ is superquadratic and $a$ and $\alpha$ are positive and almost periodic. By variational methods, we prove that if $\omega>0$ is small enough then the system admits a multibump dynamics. As a corollary we get that the system $\ddot u=u-a(t)W'(u)$ admits multibump solutions whenever $a$ belongs to an open dense subset of the class of positive almost periodic functions on $\mathbb{R}$.

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

CALDIROLI, Paolo;
1999-01-01

Abstract

In this paper we consider "slowly" oscillating perturbations of almost periodic Duffing-like systems, i.e., systems of the form $\ddot u=u-(a(t)+\alpha(\omega t))W'(u)$, $t\in\mathbb{R}$, $u\in\mathbb{R}^N$ where $W\in C^{2N}(\mathbb{R}^N,\mathbb{R})$ is superquadratic and $a$ and $\alpha$ are positive and almost periodic. By variational methods, we prove that if $\omega>0$ is small enough then the system admits a multibump dynamics. As a corollary we get that the system $\ddot u=u-a(t)W'(u)$ admits multibump solutions whenever $a$ belongs to an open dense subset of the class of positive almost periodic functions on $\mathbb{R}$.
1999
129
885
901
http://dx.doi.org/10.1017/S0308210500030985
Lagrangian systems; almost periodicity; minimax methods; slow oscillations; multibump dynamics; genericity
Alessio F.; Caldiroli P.; Montecchiari P.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2318/110415
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