Abstract
The spectrum containment of almost periodic solution of second-order neutral delay differential equations with piecewise constant of argument (EPCA, for short) of the form is considered. The main result obtained in this paper is different from that given by some authors for ordinary differential equations (ODE, for short) and clearly shows the differences between ODE and EPCA. Moreover, it is also different from that given for equation because of the difference between and .
Highlights
Introduction and Some PreliminariesDifferential equations with piecewise constant argument, which were firstly considered by Cooke and Wiener 1 and Shah and Wiener 2, combine properties of both differential and difference equations and usually describe hybrid dynamical systems and have applications in certain biomedical models in the work of Busenberg and Cooke 3
More attention has been paid to the existence, uniqueness, and spectrum containment of almost periodic solutions of this type of equations see, e.g., 4–12 and reference there in
If g1 t and g2 t are almost periodic, the module containment property mod g1 ⊂ mod g2 can be characterized in several ways see 13–16
Summary
The spectrum containment of almost periodic solution of second-order neutral delay differential equations with piecewise constant of argument EPCA, for short of the form x t px t − 1 qx 2 t 1 /2 f t is considered. The main result obtained in this paper is different from that given by some authors for ordinary differential equations ODE, for short and clearly shows the differences between ODE and EPCA. It is different from that given for equation x t px t − 1 qx t f t because of the difference between t and 2 t 1 /2.
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