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

We consider the semilinear elliptic equation u = 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 everyλ>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 . © 2007 Elsevier Inc. All rights reserved