On critical systems involving fractional Laplacian

Consider the following non-local critical systemequation(0.1){(−Δ)su−λ1u=μ1|u|2⁎−2u+αγ2⁎|u|α−2u|v|βin Ω,(−Δ)sv−λ2v=μ2|v|2⁎−2v+βγ2⁎|u|α|v|β−2vin Ω,u=0,v=0in RN∖Ω, where (−Δ)s(−Δ)s is fractional Laplacian, 00λ1,λ2,μ1,μ2,γ>0, 2⁎:=2NN−2s is a fractional Sobolev critical exponent, N>2sN>2s, α,β>1α,β>1, α+β=2⁎α+β=2⁎, and Ω is an open bounded domain in RNRN with Lipschitz boundary. Under proper conditions, we establish the existence result of the ground state solution to system (0.1).