Classification of solutions for mixed order conformally system with Hartree-type nonlinearity in ℝn.

In this paper, we consider the following mixed order conformally invariant system with Hartree-type nonlinearity: ... where 0 < s =: m + ₂^α < +∞, m is a integer, 0 < α ≤ 2, n ≥ 3, σ ∈ (0, n). We first prove the equivalence of the PDEs system and the IEs system. Then we give the classification of the nonnegative solutions to the system (0.1) by using the method of moving spheres. Finally, we prove Liouville-type theorems results for system (0.1) in the critical and supercritical-order cases (i.e. n 2 < s =: m+ ₂/α < +∞), respectively. [ABSTRACT FROM AUTHOR]