Entire nonradial solutions for non-cooperative coupled elliptic system with critical exponents in R3

We consider the following coupled elliptic system:(SN){−Δu=μ1uN+2N−2+βu2N−2vNN−2in RN,−Δv=μ2vN+2N−2+βv2N−2uNN−2in RN,u,v>0,u,v∈D1,2(RN), where N⩾3, μ1, μ2 are two positive constants and β<0 is the coupling constant. When N=3, we prove the existence of infinitely many positive nonradial solutions.