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

Wei Dai; Jingze Fu

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

Analysis of PDEs 2021-08-09 v2

Authors: Wei Dai , Jingze Fu

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.

Keywords

positive solutions tri-harmonic equations bi-harmonic equations negative exponents conformal geometry asymptotic behavior

Cite

@article{arxiv.2108.00948,
  title  = {On properties of positive solutions to nonlinear tri-harmonic and bi-harmonic equations with negative exponents},
  author = {Wei Dai and Jingze Fu},
  journal= {arXiv preprint arXiv:2108.00948},
  year   = {2021}
}

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