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 [Formula: see text] ([Formula: see text]) and bi-harmonic equations in [Formula: see text] with negative exponents. Such kind of equations arise from conformal geometry.

Keywords

• Tri-harmonic and bi-harmonic equations
• negative exponents
• nonexistence
• asymptotic behavior
• integral representation formula
• uniqueness