Usted está aquí: Multiple solutions to the pure super-critical problem for the $$p$$-Laplacian

# Multiple solutions to the pure super-critical problem for the $$p$$-Laplacian

Ponente: Sweta Tiwari
Institución: IM-UNAM
Cuándo 09/04/2015 de 10:00 a 11:00 Salón de seminarios Graciela Salicrup vCal iCal

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.