Classification of solutions to mixed order system with exponential Hartree nonlinearity and cubic nonlinearity in R3

In this paper, we are concerned with the following mixed order conformally invariant system with exponential Hartree nonlinearity and cubic nonlinearity: (Formula presented.) where p>0, u≥0, v may change sign and u satisfies the finite total curvature condition ∫R3u3(x)dx<+∞. Under extremely mild assumptions, we prove that, the classical solution (u, v) must take the unique form: (Formula presented.) for some μ>0 and x0∈R3, where I(1):=π32Γ(12)Γ(2).