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In this article, we are concerned with the following geometric equation\begin{equation}\label{MainEq} \Delta^2 u = -u^{-q} \qquad \text{in }\mathbf{R}^3 \end{equation} for $q>0$. Recently in \cite{GWZ18}, Guo, Wei andZhou have established the relationship between the radial symmetry and theexact growth rate at infinity of a positive entire solution of that equation as$1<q<3$. The aim of this paper is to obtain the similar result in the case$q>3$ thanks to the method of moving plane.

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