Radial singular solutions for the N-Laplace Equation with exponential nonlinearities

Abstract

In this paper, we consider radial distributional solutions of the quasilinear equation $-{\Delta }_{N}u=f(u)$ in the punctured open ball $ B_R\backslash\{0\}\subset \RR^N$, $N\ge 2$. We obtain sharp conditions on the nonlinearity $f$ for extending such solutions to the whole domain $B_R$ by preserving the regularity. For a certain class of noninearity $f$ we obtain the existence of singular solutions and deduce upper and lower estimates on the growth rate near the singularity.