The local behavior of positive solutions for higher order equation with isolated singularity

TL;DR

This paper investigates the local behavior of positive solutions to higher order Hardy-Henon equations near isolated singularities, establishing blow-up rates and asymptotic radial symmetry, extending previous conformally invariant equation results.

Contribution

It introduces a blow-up analysis approach for higher order equations with isolated singularities and generalizes existing results on conformally invariant equations.

Findings

Determined blow-up rates of solutions near singularities

Proved asymptotic radial symmetry of solutions

Extended Jin-Xiong's results to higher order equations

Abstract

We use blow up analysis for local integral equations to provide a blow up rates of solutions of higher order Hardy-Henon equation in a bounded domain with an isolated singularity, and show the asymptotic radial symmetry of the solutions near the singularity. This work generalizes the correspondence results of Jin-Xiong [8] on higher order conformally invariant equations with an isolated singularity.