A note on positive periodic solutions of delayed differential equations

We consider the existence of positive ω -periodic solutions for the periodic equation x ′ ( t ) = a ( t ) e x ( t ) x ( t ) − λ b ( t ) f ( x ( t − τ ( t ) ) ) , where a , b ∈ C ( R , [ 0 , ∞ ) ) are ω -periodic, ∫ 0 ω a ( t ) d t > 0 , ∫ 0 ω b ( t ) d t > 0 , f ∈ C ( [ 0 , ∞ ) , [ 0 , ∞ ) ) , and f ( u ) > 0 for u > 0 , τ ( t ) is a continuous ω -periodic function.