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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

Citations:

Zbl 1093.45001
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Full Text: DOI

References:

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