A necessary and sufficient condition for radial property of positive entire solutions of ${\Delta }^{2}u+u^{-q}=0$ in ${\mathbf{R}}^3$

Tien-Tai Nguyen

In this article, we are concerned with the following geometric equation \begin{equation}\label{MainEq} Δ^2 u = -u^{-q} \qquad \text{in } \mathbf{R}^3 \end{equation} for $q>0$. Rece…