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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 / Multiple solutions to the Bahri-Coron problem in a bounded domain without a thin neighborhood of a manifold

Multiple solutions to the Bahri-Coron problem in a bounded domain without a thin neighborhood of a manifold

Ponente: Juan Carlos Fernández
Institución: IM-UNAM
Cuándo 20/11/2014
de 12:00 a 13:00
Dónde Salón de seminarios 1
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We show that the critical problem
\[
-\Delta u=|u|^{\frac{{4}}{{N-2}}}u\ \text{in }\Omega,\quad\ u=0\ \text{on }\partial\Omega,\]
has at least
\[
\max\{\text{cat}(\Theta,\Theta\smallsetminus B_{r}M),\text{cupl}(\Theta,\Theta\smallsetminus
B_{r}M)+1\}\geq2
\]
pairs of nontrivial solutions in every domain \(\Omega\) obtained by deleting from a given bounded
smooth domain \(\Theta\subset\mathbb{R}^{N}\) a thin enough tubular neighborhood \(B_{r}M\) of a
closed smooth submanifold \(M\) of \(\Theta\) of dimension \(\leq N-2,\) where "cat" is the Lusternik-
Schnirelmann category and "cupl" is the cup-length of the pair.
This is joint work with Mónica Clapp.