Local behavior, radial symmetry and classification of solutions to weighted elliptic equations

Abstract

We study positive solutions with an isolated singularity to a class of weighted elliptic equations in $ B_1\backslash\{0\} $ and in $ \mathbb{R}^N\backslash\{0\} $. First, in $ B_1\backslash\{0\} $ we present new results on the asymptotic behavior at the singular point for positive solutions. Then in $ \mathbb{R}^N\backslash\{0\} $, we prove radially symmetric properties for positive singular solutions, and give a complete classification for these solutions.