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

We study the local properties of positive solutions of the equation $-\mathrm{\Delta }u+m\text{abs}{\mathrm{\nabla }u}^q-e^u=0$ in a punctured domain $\mathrm{\Omega }\setminus \{0\}$ of $R^N$, $N\ge 2$, 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. .