Using sub- and supersolution arguments, truncation arguments and previous results of the first author [J. Math. Anal. Appl. 21, 421-425 (1968; Zbl 0155.140)] it is proved that if h(.):R is T-periodic for some and if is continuous, , ( (in particular, if , then the equation: (1) has a T-periodic solution iff
It is also proved that if is continuous and such that: then the equation: (2) has a T-periodic solution iff and that if (in particular, if , then the equation (2) may not have a periodic solution.