Title: Critical system involving fractional Laplacian,
Abstract: In this paper, we study the following critical system with fractional
Laplacian: \begin{equation*} \begin{cases}
(-\Delta)^{s}u=
\mu_{1}|u|^{2^{\ast}-2}u+\frac{\alpha\gamma}{2^{\ast}}|u|^{\alpha-2}u|v|^{\beta}
\ \ \ \text{in} \ \ \mathbb{R}^{n},
(-\Delta)^{s}v=
\mu_{2}|v|^{2^{\ast}-2}v+\frac{\beta\gamma}{2^{\ast}}|u|^{\alpha}|v|^{\beta-2}v\
\ \ \ \text{in} \ \ \mathbb{R}^{n}, u,v\in D_{s}(\mathbb{R}^{n}). \end{cases}
\end{equation*}
By using the Nehari\ manifold,\ under proper conditions, we establish the
existence and nonexistence of positive least energy solution of the system.