Existence and uniqueness of positive periodic solutions of functional differential equations

By Xi-Lan Liu, Wan-Tong Li. 2004

47 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/d5c78564a95b020445064f02af9a96b8fce2ea1b

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In Applied Mathematics

In Computational Theory and Mathematics

In Control and Systems Engineering

Citations in the corpus

Existence, multiplicity, and dependence on a parameter for a periodic boundary value problem (2008, background): “We note that: (1) Results similar to Theorem 2.2 have been established by Li and Liu [8,9] for other types of boundary value problems.”
Nicholson's blowflies differential equations revisited: Main results and open problems (2010, methodology): “The main method used in [21,23,35–40] is the upper-lower solution method where the existence of at least one positive periodic solution is obtained by constructing a pair of upper and lower solutions and application of a fixed point theorem in cones.”