Abstract
By applying Green's function of third-order differential equation and a fixed point theorem in cones, we obtain some sufficient conditions for existence, nonexistence, multiplicity, and Lyapunov stability of positive periodic solutions for a third-order neutral differential equation.
Highlights
Neutral functional differential equations manifest themselves in many fields including biology, mechanics, and economics 1–4
These equations arise in classical “cobweb” models in economics where current demand depends on price but supply depends on the previous periodic solutions 2
The study on neutral functional differential equations is more intricate than ordinary delay differential equations
Summary
Neutral functional differential equations manifest themselves in many fields including biology, mechanics, and economics 1–4. Another approach, which will be used in this paper, is to transform the third-order equation into a corresponding integral equation and to establish the existence of positive periodic solutions based on a fixed point theorem in cones Following this path one needs an explicit representation of Green’s function which is rather intricate to compute.
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