LAUSR

Abstract Consider the following non-local critical system (0.1) { ( − Δ ) s u − λ 1 u = μ 1 | u | 2 ⁎ − 2 u + α γ 2 ⁎ | u | α − 2 u | v | β in  Ω , ( − Δ ) s v − λ 2 v = μ 2 | v | 2 ⁎ − 2 v + β γ 2 ⁎ | u | α | v | β − 2 v in  Ω , u = 0 , v = 0 in  R N ∖ Ω , where ( − Δ ) s is fractional Laplacian, 0 s 1 and all λ 1 , λ 2 , μ 1 , μ 2 , γ > 0 , 2 ⁎ : = 2 N N − 2 s is a fractional Sobolev critical exponent, N > 2 s , α , β > 1 , α + β = 2 ⁎ , and Ω is an open bounded domain in R N with Lipschitz boundary. Under proper conditions, we establish the existence result of the ground state solution to system (0.1) .