We establish the existence of distinct asymptotic profiles near the origin for positive radial solutions of the nonlinear elliptic equation
$\Delta u+(2-N-2\rho)\frac{x\cdot\nabla u}{|x|^2}+\frac{\lambda}{|x|^2}u=|x|^{\theta}u^q|\nabla u|^m$ in $B_R(0)\setminus \{0\}$, where $\rho,\lambda,\theta, m, q \in \mathbb{R}$, $m>0$, $q\geq 0$ and $m+q-1>0$. Moreover, we derive refined asymptotic behavior for each of these profiles.
This is joint work with Florica C\^ irstea (The University of Sydney).