Critical nonlinear elliptic equations with singularities and cylindrical symmetry

Abstract

Motivated by a problem arising in astrophysics we study a nonlinear elliptic equation in ${\mathbb{R}}^N$ with cylindrical symmetry and with singularities on a whole subspace of ${\mathbb{R}}^N$. We study the problem in a variational framework and, as the nonlinearity also displays a critical behavior, we use some suitable version of the Concentration-Compactness Principle. We obtain several results on existence and nonexistence of solutions.