  In this article, we study the Brezis-Nirenberg type problem of nonlinear
Choquard equation involving a fractional Laplacian \[ (-\De)^s u = \left(
\int_{\Om}\frac{|u|^{2^*_{\mu,s}}}{|x-y|^{\mu}}\mathrm{d}y
\right)|u|^{2^*_{\mu,s}-2}u +\la u \; \text{in } \Om,\] where $\Om $ is a
bounded domain in $\mathbb R^n$ with Lipschitz boundary, $\la $ is a real
parameter, $s \in (0,1)$, $n >2s$ and $2^*_{\mu,s}= (2n-\mu)/(n-2s)$ is the
critical exponent in the sense of Hardy-Littlewood-Sobolev inequality. We
obtain some existence, multiplicity, regularity and nonexistence results for
solution of the above equation using variational methods.
