Nodal cluster solutions for the Brezis-Nirenberg problem in dimensions $N\ge 7$

We show that the classical Brezis-Nirenberg problem $$\mathrm{\Delta }u+\mathrm{\mid }u{\mathrm{\mid }}^{\frac{4}{N-2}}u+\epsilon u=0,\text{mbox}in\mathrm{\Omega },u=0,\text{mbox}on\mathrm{\partial }\mathrm{\Omega }$$ admits nodal solutions clustering around a point on the boundary of $\mathrm{\Omega }$ as $\epsilon \to 0$, for smooth bounded domains $\mathrm{\Omega }\subset {\mathbb{R}}^N$ in dimensions $N\ge 7$.