Existence and uniqueness of positive periodic solutions of functional differential equations

Abstract

In this paper we consider the existence and uniqueness of positive periodic solution for the periodic equation y′( t)=− a( t) y( t)+ λh( t) f( y( t− τ( t))). By the eigenvalue problems of completely continuous operators and theory of α-concave or − α-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 y λ ( t) of the above equation depends continuously on the parameter λ. Finally, as an application, we obtain sufficient condition for the existence of positive periodic solutions of the Nicholson blowflies model.