This paper deals with the following fractional Laplacian system with critical exponent: (−Δ)su=λ1u+μ1|u|2s∗−2u+β|u|2s∗2−2u|v|2s∗2,inΩ,(−Δ)sv=λ2v+μ2|v|2s∗−2v+β|v|2s∗2−2v|u|2s∗2,inΩ,u=v=0,inRN\Ω,$$ \left\{\begin{array}{ll}{\left(-\Delta \right)}^su={\lambda}_1u+{\mu}_1{\left|u\right|}^{2_s^{\ast }-2}u+\beta {\left|u\right|}^{\frac{2_s^{\ast }}{2}-2}u{\left|v\right&#x...
