Classification of positive singular solutions for a class of semilinear elliptic systems

Abstract

This paper is concerned with the behavior near an isolated singularity of positive radial solutions of the semilinear elliptic system $$ \begin{cases} -\Delta u=\vert v\vert^{p-1}v \\ -\Delta v=\vert u\vert^{q-1}u, \end{cases} \text{in}\ \ \Omega^*\subset\Bbb R^N, $$ where $\Omega^*$ denotes the punctured unit ball in $\Bbb R^N\ (N\ge 3)$ and $(p,q)$ lies in the region between the two critical hyperbolas $\mathcal{H}_1$ and $\mathcal{H}_2$ defined below.