where are continuous -periodic functions with positive average, and .
The main result of this paper establishes sufficient conditions to ensure the existence of at least one -periodic solution for the second order delay-differential equation
Here, are continuous and -periodic, and the continuous function is -periodic in for all .
The Green function for the periodic problem associated to the ordinary differential equation is used to define a suitable abstract operator whose fixed points are the periodic solutions of (1). Then, a fixed point theorem due to Krasnosel’skii is applied to get the desired existence result. Under an additional condition, this operator is shown to be a contraction, and therefore the -periodic solution is unique.