The paper is devoted to the solvability of a singular Dirichlet boundary value problem of the form
The nonlineearity is continuous, can change its sign and can have time singularities at and and a space singularity at . Moreover, may be superlinear in its second variable for and sublinear in its third variable for . The existence of a solution such that for and is proved. The proof is based on the Leray-Schauder fixed-point theorem and on the lower and upper solutions method. The author was motivated by P. Habets and F. Zanolin [J. Math. Anal. Appl. 181 No.3, 684-700 (1994; Zbl 0801.34029)] and by R.P. Agarwal and D. O’Regan [J. Differ. Equations 143 No.1, 60-95 (1998; Zbl 0902.34015)].