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

Wei Dai, Jingze Fu

Published 2021-08-02Version 1

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