Radial symmetry and uniqueness for positive solutions of a Schrödinger type system

In this paper, we consider positive solutions of an integral system arising from higher order semilinear Schrödinger type systems in RnRn. We are able to establish the radial symmetry and monotonicity theorem for those positive solutions by means of the new moving-plane method proposed by Chen–Li–Ou [W. Chen, C. Li, B. Ou, Classification of solutions for an integral equation, Commun. Pure Appl. Math. 59 (3) (2006) 330–343] coupled with a Sobolev imbedding theorem involving Bessel potentials. We also obtain the uniqueness theorem for some radial symmetric solutions.