Existence of sharp asymptotic profiles of singular solutions to an elliptic equation with a sign-changing non-linearity

Florica C. Cîrstea, Frédéric Robert and Jérôme Vétois

Abstract

The first two authors [Proc. Lond. Math. Soc. (3) 114(1):1–34, 2017] classified the behaviour near zero for all positive solutions of a perturbed elliptic equation with a critical Hardy-Sobolev growth. It was shown in the op. cit. that the positive solutions with a non-removable singularity at zero could exhibit up to three different singular profiles, although their existence was left open. In the present paper, we settle this question for all three singular profiles in the maximal possible range.

Keywords: Isolated singularities, Hardy-Sobolev potential, singular solutions, removable singularities.

AMS Subject Classification: Primary 35J91; secondary 35A20, 35J75, 35J60.