This paper deals with existence, uniqueness and regularity of positive generalized solutions of singular nonlinear equations of the form $-\Delta u + a(x)u = h(x)u^{-\gamma}$ in $\mathbf{R}^N$ where $a,h$ are given, not necessarily continuous functions, and $γ$ is a positive number. We explore both situations where $a,h$ are radial functions, with $a$ being eventually identically zero, and cases where no symmetry is required from either $a$ or $h$ . Schauder′s fixed point theorem, combined with penalty arguments, is exploited.