  We establish several results related to existence, nonexistence or
bifurcation of positive solutions for a Dirichlet boundary value problem with
in a smooth bounded domain. The main feature of this paper consists in the
presence of a singular nonlinearity, combined with a convection term. Our
approach takes into account both the sign of the potential and the decay rate
around the origin of the singular nonlinearity. The proofs are based on various
techniques related to the maximum principle for elliptic equations.
