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.