Decay rate and radial symmetry of the exponential elliptic equation

Sunghoon Kim, Kin Ming Hui

Let $n\ge 3$, $\alpha$, $\beta \in \mathbb{R}$, and let $v$ be a solution $\Delta v+\alpha e^v+\beta x\cdot \nabla e^v=0$ in ${\mathbb{R}}^n$, which satisfies the conditions $\lim_{R\to\infty}\frac{1}{\log R}\i…