A note on positive periodic solutions of delayed differential equations

We consider the existence of positive ωω-periodic solutions for the periodic equation x′(t)=a(t)ex(t)x(t)−λb(t)f(x(t−τ(t))), where a,b∈C(R,[0,∞))a,b∈C(R,[0,∞)) are ωω-periodic, ∫0ωa(t)dt>0, ∫0ωb(t)dt>0, f∈C([0,∞),[0,∞))f∈C([0,∞),[0,∞)), and f(u)>0f(u)>0 for u>0u>0, τ(t)τ(t) is a continuous ωω-periodic function.