Existence and nonexistence results for quasilinear elliptic equations involving the p-laplacian

The paper deals with the study of a quasilinear elliptic equation involving the $p$-laplacian with a Hardy-type singular potential and a critical nonlinearity. Existence and nonexistence results are first proved for the equation with a concave singular term. Then we study the critical case related to Hardy inequality, providing a description of the behavior of radial solutions of the limiting problem and obtaining existence and multiplicity results for perturbed problems through variational and topological arguments.