The author considers the singular boundary value problem
where , on , , or and or . Under the assumption that is bounded or fulfills the classical sign conditions in the second variable and the Nagumo-type conditions in the third variable, he proves the existence. The typical conditions imposed on and are
The proof is based on the upper and lower solutions method and the Schauder fixed point theorem. The results complete the earlier ones by the author in [Nonlinear Anal., Theory Methods Appl. 21, 153-159 (1993; Zbl 0790.34027)].