A Relation Between the Domain Topology and the Number of Minimal Nodal Solutions for a Quasilinear Elliptic Problem

We consider the quasilinear problem $-\mbox{div}(|\nabla u|^{p-2}\nabla u)+ |u|^{p-2}u = |u|^{q-2}u$ in $\Omega$, $u=0$ on $\partial \Omega$ where $\Omega \subset \mathbb{R}^N$ is a bounded smooth domain, $1 < p < N$ and $p