  In this paper, we are inspired by Ng\^{o}, Nguyen and Phan's [15] study of
the pointwise inequality for positive $C^{4}$-solutions of biharmonic equations
with negative exponent by using the growth condition of solutions. They propose
an open question of whether the growth condition is necessary to obtain the
pointwise inequality. We give a positive answer to this open question. We
establish the following local pointwise inequality $$-\frac{\Delta
u}{u}+\alpha\frac{|\nabla u|^{2}}{u^{2}}+\beta
u^{-\frac{q+1}{2}}\leq\frac{C}{R^{2}}$$ for positive $C^{4}$-solutions of the
biharmonic equations with negative exponent $$-\Delta^{2}u=u^{-q} \ in \
B_{R}$$ where $B_{R}$ denotes the ball centered at $x_{0}$ with radius $R$,
$n\geq3$, $q>1$, and some constants $\alpha\geq0$, $\beta>0$, $C>0$.

Analysis of PDEs