Existence and uniqueness of positive periodic solutions of functional differential equations

In this paper we consider the existence and uniqueness of positive periodic solution for the periodic equation <f>y′(t)=−a(t)y(t)+λh(t)f(y(t−τ(t))).</f> By the eigenvalue problems of completely continuous operators and theory of <f>α</f>-concave or <f>−α</f>-convex operators and its eigenvalue, we establish some criteria for existence and uniqueness of positive periodic solution of above functional differential equations with parameter. In particular, the unique solution <f>yλ(t)</f> of the above equation depends continuously on the parameter <f>λ.</f> Finally, as an application, we obtain sufficient condition for the existence of positive periodic solutions of the Nicholson blowflies model. [Copyright &y& Elsevier]