Multiple solutions to the pure super-critical problem for the \(p\)-Laplacian
Ponente: Sweta Tiwari
Institución: IM-UNAM
Institución: IM-UNAM
Cuándo |
09/04/2015 de 10:00 a 11:00 |
---|---|
Dónde | Salón de seminarios Graciela Salicrup |
Agregar evento al calendario |
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We present some existence and multiplicity results of positive and sign changing
solutions to the problem
\[
-\Delta_pv=|v|^{q-2}v\text{ in }\Omega,\ v=0\text{ on }\partial\Omega,
\]
in some bounded smooth domain \(\Omega\) in \(\mathbb{R}^N\) , where
\(\Delta_pv:= \mathrm{div}\,(|\nabla v|^{p-2}\nabla v)\) is the
\(p\)-Laplace operator, \(1 < p < N\) and \(q > p^∗ :=
\frac{Np}{N−p}\) is super-critical.
As far as we know, these are the first existence results for the pure
super-critical quasilinear problem.