A complete classification of the behaviour near zero of all non-negative solutions of -Δu+uq=0 in the punctured unit ball B1(0)\{0} in RN (N≥3) is due to Veron (1981) for 1<q<N∕(N-2), and Brezis-Veron (1980/81) for q≥N∕(N-2). In this talk, we extend these results to nonlinear elliptic equations in divergence form -∇⋅(A(|x|)∇u)+uq=0 with q>1. Here, A denotes a positive C1(0,1] function which is regularly varying at zero with index in (2-N,2). We show that zero is a removable singularity for all positive solutions if and only if Φ∉Lq(B1(0)), where Φ denotes the fundamental solution of -∇⋅(A(|x|)∇u)=δ0 in the sense of distributions on B1(0), and δ0 is the Dirac mass at 0. We also completely classify the isolated singularities in the more delicate case that Φ∈Lq(B1(0)). This is joint work with B. Brandolini, F. Chiacchio and C. Trombetti.