On properties of positive solutions to nonlinear tri-harmonic and bi-harmonic equations with negative exponents

Abstract

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 ${\mathbb{R}}^n$ ($n\ge 2$) and bi-harmonic equations in ${\mathbb{R}}^2$ with negative exponents. Such kind of equations arise from conformal geometry.