Isolated singularities for weighted quasilinear elliptic equations

Florica C. Cîrstea and Yihong Du

Abstract

We classify all the possible asymptotic behaviour at the origin for positive solutions of weighted quasilinear elliptic equations. Our central result provides a sharp extension of a well-known theorem of Friedman and Veron given for the special case of power nonlinearities. Our approach relies on the regular variation theory and a new perturbation method for constructing sub- and super-solutions for the equation.

Keywords: quasilinear elliptic equations, isolated singularities, regular variation theory, sub-super-solutions method.

AMS Subject Classification: Primary 35J25; secondary 35B40, 35J60.