Critical nonlinear elliptic equations with singularities and cylindrical symmetry, preprint SISSA

We study the existence of solutions to a semi-linear elliptic equation in the whole space. The equation has a cylindrical symmetry and we find cylindrical solutions. The main features of the problem are that the potential has a large set of singularities (i.e. a subspace), and that the nonlinearity has a double power-like behaviour, sub-critical at infinity and super-critical near the origin. We also show that our results imply the existence of solitary waves with non-vanishing angular momentum for nonlinear evolution equations of Schrödinger and Klein-Gordon type. Stampato nel mese di Aprile 2005 presso il Centro Stamp