A field-theoretical model describing simple one-species reaction-diffusion systems [A+A→O (inert) or A+A→A] with an external source is analyzed from a renormalization-group point of view. It is shown that when the dimension of the system is larger than the upper critical dimension du=2, the behavior of the system is governed by a trivial fixed point dominated by diffusion. Below the upper critical dimension, a line of fixed points governs the behavior. Reaction and diffusion processes play an equally important role resulting in a so-called anomalous kinetic behavior. This approach confirms previous scaling arguments. Possible generalizations to more complicated models are discussed.