Periodic solutions of logistic equations with time delay

A new criterion is established for the existence of positive periodic solutions to the following delay logistic equation: u′(t)=u(t)[r(t)−a(t)u(t)+b(t)u(t−τ)]u′(t)=u(t)[r(t)−a(t)u(t)+b(t)u(t−τ)] where r(t)r(t), a(t)a(t), b(t)b(t) are periodic continuous functions, a(t)>0a(t)>0, b(t)≥0b(t)≥0 and r(t)r(t) has positive average.