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
Qinian Jin. YanYan Li. Haoyuan Xu. "Symmetry and asymmetry: the method of moving spheres." Adv. Differential Equations 13 (7-8) 601 - 640, 2008. https://doi.org/10.57262/ade/1355867331
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