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

Pedro M. Girão, Miguel Ramos

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 $Ω…