Symmetry of ground states for a semilinear elliptic system

Zou, Henghui

doi:10.1090/S0002-9947-99-02526-X

Symmetry of ground states for a semilinear elliptic system
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Trans. Amer. Math. Soc. 352 (2000), 1217-1245 Request permission

Abstract:

Let $n\ge 3$ and consider the following system \begin{equation*} \Delta \mathbf {u}+\mathbf {f}(\mathbf {u})=0,\quad \mathbf {u}>0,\qquad x\in \mathbf {R}^n.\end{equation*} By using the Alexandrov-Serrin moving plane method, we show that under suitable assumptions every slow decay solution of (I) must be radially symmetric.

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