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

We consider the semilinear elliptic equation Delta u = h(u) in Omega\{0}, where Omega is an open subset of R-N (N >= 2) containing the origin and h is locally Lipschitz continuous on [0, infinity), positive in (0, infinity). We give a complete classification of isolated singularities of positive solutions when It varies regularly at infinity of index q is an element of (1, C-N) (that is, lim(u ->infinity)(lambda u)/h(u) =lambda(q), for every lambda > 0), where C-N denotes either N/(N - 2) if N >= 3 or infinity, if N = 2. Our result extends a well-known theorem of Veron for the case h (u) = u(q). (C) 2007 Elsevier Inc. All rights reserved.