Oscillation and Periodicity of a Second Order Impulsive Delay Differential Equation with a Piecewise Constant Argument

Oscillation Criteria of Certain Third-Order Differential Equation with Piecewise Constant Argument

Almost-Periodic Weak Solutions of Second-Order Neutral Delay-Differential Equations with Piecewise Constant Argument

Differential equations with piecewise constant argument, which were firstly considered by Cooke and Wiener 1 , and Shah and Wiener 2 , usually describe hybrid dynamical systems a combination of continuous and discrete and so combine properties of both differential and difference equations. Over the years, great attention has been paid to the study of the existence of almost-periodic-type soluti...

On Oscillation of a Second Order Impulsive Linear Delay Differential Equation

Global dynamics of a differential equation with piecewise constant argument

Several aspects of global dynamics are studied for the scalar differential-difference equation εẋ(t) + x(t) = f (x([t])), 0 < ε 1, where [·] is the integer part function. The equation is a particular case of the special discretization (discrete version) of the singularly perturbed differential delay equation εẋ(t)+ x(t) = f (x(t−1)). Sufficient conditions for the invariance, global stability of...

Oscillation by impulses for a second-order delay differential equation

We consider a certain second-order nonlinear delay differential equation and prove that the all solutions oscillate when proper impulse controls are imposed. An example is given. c © 2006 Elsevier Science Ltd. All rights reserved. Keywords—Delay differential equations, Second-order, Nonlinear, Oscillation, Impulses.