Asymptotic Behavior of Solutions of Δu+K(z)eu=0 in a Punctured Disc

We give necessary and sufficient conditions for the solutions of https://www.w3.org/1998/Math/MathML">Δu+Keu=0https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429064593/1178e5ac-b8c1-4916-83b8-0e4e91098d1a/content/eq363.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> in the punctured unit disc to have asymptotic radial symmetry, where K is a measurable, bounded, non-negative function.