## Radial symmetry and uniqueness for positive solutions of a Schrödinger type system.(English)Zbl 1165.35372

Summary: We consider positive solutions of an integral system arising from higher order semilinear Schrödinger type systems in $$\mathbb{R}^n$$. 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 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.

### MSC:

 35J60 Nonlinear elliptic equations

### Keywords:

elliptic system; radial symmetry; monotonicity; uniqueness

Zbl 1093.45001
Full Text:

### References:

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