Singularities and asymptotics of solutions of the Chandrasekhar-Hailton-Jacobi equation

Abstract

We study the local properties of positive solutions of the equation $-\Delta u+ m\abs{\nabla u}^q-e^{u}=0$ in a punctured domain $\Omega\setminus\{0\}$ of $R^N$, $N\geq 2$, where $m$ is a positive parameter and $q>1$. We study particularly the existence of solutions with an isolated singularity and the local behaviour of such singular solutions. .