Oscillation Test for Linear Delay Differential Equation with Nonmonotone Argument

Oscillation of a Linear Delay Impulsive Differential Equation

The main result of the paper is that the oscillation (non-oscillation) of the impulsive delay differential equation ẋ(t) + m ∑ k=1 Ak(t)x[hk(t)] = 0, t ≥ 0, x(τj) = Bjx(τj − 0), lim τj = ∞ is equivalent to the oscillation (non-oscillation) of the equation without impulses ẋ(t) = m ∑

Nonlinear oscillation of certain third-order neutral differential equation with distributed delay

The authors obtain necessary and sufficient conditions for the existence of oscillatory solutions with a specified asymptotic behavior of solutions to a nonlinear neutral differential equation with distributed delay of third order. We give new theorems which ensure that every solution to be either oscillatory or converges to zero asymptotically. Examples dwelling upon the importance of applicab...

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.

Oscillation of High Order Linear Functional Differential Equation with Impulses

We study the solutions to high-order linear functional differential equations with impulses. We improve previous results in the oscillation theory for ordinary differential equations and obtain new criteria on the oscillation of solutions.

On Oscillation of a Second Order Impulsive Linear Delay Differential Equation