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Existence and uniqueness of positive periodic solutions of functional differential equations
Authors:Xi-Lan Liu  Wan-Tong Li
Institution:a Department of Mathematics, Lanzhou University, Lanzhou, Gansu 730000, People's Republic of China
b Department of Mathematics, Yanbei Normal College, Datong, Shanxi 037000, People's Republic of China
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(tτ(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 yλ(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.
Keywords:Functional differential equation  Positive periodic solution  Cone  Delay  Eigenvalue  Uniqueness
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