Positive solutions of anisotropic Yamabe-type equations in $\mathbb {R}^n$

Abstract

We study entire positive solutions to the partial dierential equation in R n xu + ( + 1) 2 |x| 2 yu = | x| 2 u n+2 n 2, where x 2 R 2 , y 2 R n 2 , n 3 and > 0. We classify positive solutions with second order derivatives satisfying a suitable growth near the set x = 0.