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

Abstract

In this paper, we consider the following mixed order conformally invariant system with Hartree-type nonlinearity : [Formula: see text] where [Formula: see text], [Formula: see text] is a integer, [Formula: see text], [Formula: see text], [Formula: see text]. 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. [Formula: see text]), respectively.