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Usted está aquí: Inicio / Actividades / Seminarios / Seminario de Ecuaciones Diferenciales No Lineales (SEDNOL) / Actividades del Seminario de Ecuaciones Diferenciales No Lineales / Sign-changing solutions to a partially periodic nonlinear Schrödinger equation in domains with unbounded boundary

Sign-changing solutions to a partially periodic nonlinear Schrödinger equation in domains with unbounded boundary

Ponente: Yéferson Fernández
Institución: IM-UNAM
Tipo de Evento: Investigación
Cuándo 26/05/2016
de 10:00 a 11:00
Dónde Salón 2
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We consider the problem

\begin{equation*}
-\Delta u + (V_\infty + V (x)) u = |u|^{p-2} u,\qquad    u \in  H_0^1 (\Omega ),
\end{equation*}
where \(\Omega \) is either \(\mathbb{R}^N\) or a smooth domain in \(\mathbb{R}^N\) with unbounded boundary, \(N\ge  3\), \(V_\infty > 0\), \(V \in  \mathcal{C}^0 (\mathbb{R}^N )\), \(\inf_{\mathbb{R}^N}V>-V_\infty\)  and \(2 < p < \frac{2N}{N-2}\). We assume \(V\) is periodic in the first \(m\) variables, and decays exponentially to zero in the remaining ones. We also assume that \(\Omega \) is periodic in the first \(m\) variables and has bounded complement in the other ones. Then, assuming that \(\Omega \) and \(V\) are invariant under some suitable group of symmetries on the last \(N - m\) coordinates of \(\mathbb{R}^N\), we establish existence and multiplicity of sign-changing solutions to this problem.

This is joint work with Mónica Clapp (IM-UNAM).