A complete classification of the isolated singularities for nonlinear elliptic equations with inverse square potentials

Florica C. Cîrstea

Abstract

In this paper we consider a broad class of nonlinear elliptic equations in a punctured domain and give a complete classification of the behaviour near an isolated singularity for all positive solutions. An important feature of our study lies in the incorporation of inverse square potentials and weighted nonlinearities, whose asymptotic behaviour is modeled by regularly varying functions. In particular, we find sharp conditions such that the singularity is removable for all non-negative solutions, thus resolving an open question of Vazquez and Veron (1985).

Keywords: Nonlinear elliptic equations, isolated singularities, regular variation theory, inverse square potentials.

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