Singularities for a 2-Dimensional Semilinear Elliptic Equation with a Non-Lipschitz Nonlinearity

We study the limit behaviour of solutions of the semilinear elliptic equation with a non-Lipschitz nonlinearity on the right-hand side. When σ+2 2 we give a complete classification of the types of singularities asx→0 andx→∞ which in the rescaled form are essentially non-analytic and, even more, notC∞. The proof is based on the asymptotic study of the corresponding evolution dynamical system and the Sturmian argument on zero set analysis.