Singularities for a 2-dimensional semilinear elliptic equation with a non-Lipschitz nonlinearity

We study the limit behaviour of solutions of the semilinear elliptic equati on Delta u = \x\(sigma) \u\ (q-1) u in R-2, q epsilon (0,1), sigma epsilon R, with a non-Lipschitz nonlinearity on the right-hand side; When \sigma + 2\ less than or equal to 2 we give a complete classification of the types of s ingularities as x --> 0 and x --> infinity which in the rescaled form are e ssentially non-analytic and, even more, not C-infinity. The proof is based on the asymptotic study of the corresponding evolution dynamical system and the Sturmian argument on zero set analysis. (C) 1999 Academic Press.