  In this paper, we investigate various properties (e.g., nonexistence,
asymptotic behavior, uniqueness and integral representation formula) of
positive solutions to nonlinear tri-harmonic equations in $\mathbb{R}^{n}$
($n\geq2$) and bi-harmonic equations in $\mathbb{R}^{2}$ with negative
exponents. Such kind of equations arise from conformal geometry.
