Existence of non-radial solutions of an elliptic system

In this paper, we study the following elliptic system −Δu=μ1u3+βuv2,x∈Ω−Δv=μ2v3+βu2v,x∈Ωu,v>0,x∈Ω,u=v=0,x∈∂Ω,where Ω⊂R4 is an annulus, μ1,μ2>0 and β>0. By variational method, we prove that the system has a non-radial solution.