Sharp asymptotic profiles for singular solutions to an elliptic equation with a sign-changing nonlinearity

Florica C. Cîrstea, Frédéric Robert

Abstract

In this paper, we provide a full description of the profile of the positive solutions near an isolated singularity for a class of elliptic equations involving critical Hardy–Sobolev type potentials and a pure power non-linearity. Because of the interaction between these two terms, we show that two new singular behaviors may occur.

Keywords: singular solutions, semilinear elliptic equations, non-removable singularities.

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