Abstract
AbstractIn this paper we consider the following elliptic system in ℝ3where K(x), α(x) are non-negative real functions defined on ℝ3so that. When K(x) ≡ K∞and α(x) ≡ α∞we have already proved the existence of a radial ground state of the above system. Here, by using a new version of the moving plane method, we show that all positive solutions of the above system with K(x) ≡ K∞and a(x) ≡ α∞are radially symmetric and the linearized operator around a radial ground state is also non-degenerate. Using these results we further prove, under additional assumptions on K(x) and α(x), but not requiring any symmetry property on them, the existence of a positive solution for the system.
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