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

In this paper, we consider positive solutions of an integral system arising from higher order semilinear Schrödinger type systems in R n . 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.