Existence of maximal and minimal periodic solutions for first-order functional differential equations

One important question in population models is whether periodic solutions exist and whether they are bounded between minimal and maximal solutions. This paper deals with the existence of maximal and minimal periodic solutions for the periodic solutions of a first-order functional differential equation y ′ ( t ) = − a ( t ) y ( t ) + f ( t , y ( t − τ ( t ) ) ) by using the method of lower and upper solutions.