Asymptotic behavior of solutions of semilinear elliptic equations near an isolated singularity

We consider the semilinear elliptic equation Δu=h(u) in Ω∖{0}, where Ω is an open subset of RN (N⩾2) containing the origin and h is locally Lipschitz continuous on [0,∞), positive in (0,∞). We give a complete classification of isolated singularities of positive solutions when h varies regularly at infinity of index q∈(1,CN) (that is, limu→∞h(λu)/h(u)=λq, for every λ>0), where CN denotes either N/(N−2) if N⩾3 or ∞ if N=2. Our result extends a well-known theorem of Véron for the case h(u)=uq.