Symmetry of ground states for a semilinear elliptic system
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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.References
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- H. Zou, in preparation.
Additional Information
- Received by editor(s): April 4, 1997
- Received by editor(s) in revised form: October 20, 1997
- Published electronically: September 20, 1999
- Additional Notes: Research supported in part by NSF Grants DMS-9418779 and DMS-9622937, an Alabama EPSCoR grant and a faculty research grant of the University of Alabama at Birmingham
- © Copyright 1999 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 352 (2000), 1217-1245
- MSC (1991): Primary 35B40, 35J60
- DOI: https://doi.org/10.1090/S0002-9947-99-02526-X
- MathSciNet review: 1675167