  We study the problem \[ -\De u =
\left(\int_{\Om}\frac{|u(y)|^{2^*_{\mu}}}{|x-y|^{\mu}}dy\right)|u|^{2^*_{\mu}-2}u,
\; \text{in}\; \Om,\quad
  u = 0 \; \text{ on } \pa \Om , \] where $\Om$ is a smooth bounded domain in
$\mathbb{R}^N( N\geq 3)$, $2^*_{\mu}=\frac{2N-\mu}{N-2}$. we prove the
existence of a positive solution of the above problem in an annular type domain
when the inner hole is sufficiently small.

Analysis of PDEs