Sign changing solutions for elliptic equations with critical growth in cylinder type domains

Abstract

We prove the existence of positive and of nodal solutions for $-\Delta u=|u{|}^{p-2}u+\mu |u{|}^{q-2}u$, $u\in {\mathrm{H}}_0^1(\Omega )$, where $\mu >0$ and $2<q<p=2N(N-2)$, for a class of open subsets $\Omega$ of ${\mathbb{R}}^N$ lying between two infinite cylinders.

13 pages