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

Girão, Pedro; Ramos, Miguel

ESAIM: Control, Optimisation and Calculus of Variations, Tome 7 (2002), pp. 407-419.

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

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