Summary: In this note we investigate the existence of decaying positive and radial solutions of the following problem \[ \Delta u+F_\nu \bigl( |x|, u\bigr)_+= 0\quad\text{in}\quad \mathbb{R}^n;\;n\geq 3; \;\lim_\infty u(x)= 0, \]
\[ F_\nu\bigl( |x|, u\bigr):= f\bigl(|x|\bigr)u^{-\gamma}+ \nu g\bigl(|x|\bigr) u^q;\;\nu,\gamma, q>0, \] for \(f,g\in C ([0, \infty))\); \(f\) a positive function. A method of sub-super-solutions for radial solutions of equations with decreasing nonlinearity is established. As well as important in its own right, this method is used for our existence theorems.