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

Wei Dai; Jingze Fu

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arXiv · 2108.00948

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

Wei Dai·Jingze Fu

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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 $\mathbb{R}^{n}$ ($n\geq2$) and bi-harmonic equations in $\mathbb{R}^{2}$ with negative exponents. Such kind of equations arise from conformal geometry.

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Wei Dai, Jingze Fu. 2021-08-02. On properties of positive solutions to nonlinear tri-harmonic and bi-harmonic equations with negative exponents. https://arxiv.org/abs/2108.00948

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