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arXiv · 2210.04619

Super polyharmonic property and asymptotic behavior of solutions to the higher order Hardy-H\'enon equation near isolated singularities

Xia Huang·Yuan Li·Hui Yang
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Abstract

In this paper, we are devoted to studying the positive solutions of the following higher order Hardy-H\'enon equation $$ (-\Delta)^{m}u=|x|^{\alpha}u^{p} \quad\mbox{in}~ B_{1}\setminus\{0\}\subset\mathbb{R}^{n} $$ with an isolated singularity at the origin, where $\alpha>-2m$, $m\geq1$ is an integer and $n>2m$. For $1 0$ is an exact constant.

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Xia Huang, Yuan Li, Hui Yang. 2022-10-10. Super polyharmonic property and asymptotic behavior of solutions to the higher order Hardy-H\'enon equation near isolated singularities. https://arxiv.org/abs/2210.04619

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