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Existence of sign changing solutions for some critical problems on $\mathbb R^N$
The main purpose of this paper is to construct families of positive and changing-sign solutions for both
the slightly subcritical and slightly supercritical equations
$-\Delta u+V(x)u=N(N-2)|u|^{\frac{4}{N-2}\pm\varepsilon}u$ in $\mathbb R^N,$
which blow-up and concentrate at different points of $\mathbb R^N$ as $\varepsilon$ goes to 0, under certain conditions on
the potential $V.$