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.

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