On trichotomy of positive singular solutions associated with the Hardy-Sobolev operator

Nirmalendu Chaudhuri, Florica C. Cirstea

Abstract

In this paper we consider a class of semilinear elliptic equations in a punctured domain and analyse the influence of the Hardy potential on the behaviour of positive solutions near zero. We reveal a trichotomy of positive singular solutions for superlinear nonlinearities that are subcritical, where the fundamental solutions associated with the Hardy-Sobolev operator play a crucial role.

Keywords: semilinear elliptic equations, isolated singularities, Hardy-Sobolev operator, Hardy inequality.

AMS Subject Classification: Primary 35J60; secondary 35B40.