Isolated singularities of solutions of a 2-D diffusion equation with mixed reaction

Abstract

We study the local properties of positive solutions of the equation $-\Delta u+ae^{bu}=m|\nabla u|^q$ in a punctured domain $\Omega\setminus\{0\}$ of $\bf R^2$ where $m,a,b$ are positive parameters and $q>1$. We study particularly the existence of solutions with an isolated singularity and the local behaviour of such singular solutions.