A Sharp Oscillation Criterion for a Linear Differential Equation with Variable Delay

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 ∑

On an Oscillation Criterion for a Second Order Linear Quasi-differential Equation

In this paper we give an oscillation criterion for the quasi-differential equation (py')' + qy = 0. The results include a generalisation of an oscillation theorem of Hartman. We also give a necessary and sufficient condition for oscillation.

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.

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...

On Oscillation of a Second Order Impulsive Linear Delay Differential Equation