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Multi-clustered solutions for a forced pendulum equation

Ponente: Dora Salazar
Institución: Universidad de Chile
Tipo de Evento: Investigación
Cuándo 17/03/2016
de 10:00 a 11:00
Dónde Salón 2
Agregar evento al calendario vCal

We consider the singularly perturbed forced pendulum equation
\varepsilon^2 u_{\varepsilon}^{\prime\prime}+\sin (u_{\varepsilon})=\varepsilon^2\alpha(t) u_{\varepsilon}+\varepsilon^2\beta(t) u_{\varepsilon}^{\prime}\qquad \text{in } (-L,L),
where \(\alpha,\beta\in C^2([-L,L],\mathbb{R})\) and  \(u_{\varepsilon}\) represents the angle of the pendulum.

We shall present some recent results concerning the asymptotic behaviour of high energy solutions of this equation as the parameter \(\varepsilon\) approaches zero.

We shall also  prove the existence of a family of solutions having a prescribed  asymptotic profile and exhibiting a highly rotatory behaviour alternated with a highly oscillatory behaviour in some open subsets of the domain. The proof of these results relies on a combination of the Nehari finite dimensional reduction with the topological degree theory.

This is a joint work with Salomé Martínez (Universidad de Chile).