Positive periodic solutions of nonautonomous functional differential systems

Considered is the periodic functional differential system with a parameter, x (t) = A(t, x(t))x(t) + λf (t , xt ). Using the eigenvalue problems of completely continuous operators, we establish some criteria on the existence of positive periodic solutions. Moreover, we apply the results to a couple of population models and obtain sufficient conditions for the existence of positive periodic solutions, which are compared with existing ones. © 2006 Elsevier Inc. All rights reserved