On $p$-Laplace equations with a critical Hardy-Sobolev exponent and a Hardy potential

TL;DR

This paper classifies all positive solutions in a specific function space for a class of p-Laplace equations involving critical Hardy-Sobolev exponents and Hardy potentials, advancing understanding of their solution structure.

Contribution

It provides a complete classification of positive solutions for p-Laplace equations with critical Hardy-Sobolev exponents and Hardy potentials, a problem not fully addressed before.

Findings

Complete classification of positive solutions

Identification of solution structure

Extension of known results to Hardy potential cases

Abstract

For $N\ge2$ and $1<p<N$, we classify all positive $\mathcal{D}^{1,p}(\mathbb{R}^N)$-solutions to $p$-Laplace equations with a critical Hardy-Sobolev exponent and a Hardy potential.