Summary: We consider positive solutions of an integral system arising from higher order semilinear Schrödinger type systems in
. 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 W. Chen, C. Li
and B. Ou
[Commun. Pure Appl. Math. 59, No. 3, 330–343 (2006; Zbl 1093.45001
); corrigendum 59, No. 7, 1064 (2006)] coupled with a Sobolev imbedding theorem involving Bessel potentials. We also obtain the uniqueness theorem for some radial symmetric solutions.