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2008 Symmetry and asymmetry: the method of moving spheres
Qinian Jin, YanYan Li, Haoyuan Xu
Adv. Differential Equations 13(7-8): 601-640 (2008).

Abstract

This paper consists of two parts. The first part concerns a question raised by Véron on the symmetry property of positive solutions of the semilinear elliptic equation $$ \Delta u+\frac{c}{|x|^2} u +u^{(n+2)/(n-2)}=0 \quad \mbox{in } \mathbb {R}^n\setminus \{0\}. $$ The second part concerns some nonlinear elliptic equations on the unit sphere ${\mathbb S}^n$. By the method of moving spheres and the global bifurcation theory, we obtain various symmetry, asymmetry, and non-existence results.

Citation

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Qinian Jin. YanYan Li. Haoyuan Xu. "Symmetry and asymmetry: the method of moving spheres." Adv. Differential Equations 13 (7-8) 601 - 640, 2008.

Information

Published: 2008
First available in Project Euclid: 18 December 2012

zbMATH: 1201.35099
MathSciNet: MR2479025

Subjects:
Primary: 35J60
Secondary: 35A25, 35B05

Rights: Copyright © 2008 Khayyam Publishing, Inc.

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Vol.13 • No. 7-8 • 2008
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