On Oscillation of a Second Order Impulsive Linear Delay Differential Equation

On Oscillation of a Second Order Impulsive Linear Delay Differential Equation

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 the Oscillation of Second Order Linear Impulsive Differential Equations

For the second order linear impulsive differential equation with oscillatory coefficient ⎧⎨ ⎩ (r(t)x′(t))′ +h(t)x(t) = 0, t = tk, tk t0, k = 1,2, · · · , x(t+ k ) = akx(tk), x ′(t+ k ) = bkx ′(tk), k = 1,2, · · · , x(t+ 0 ) = x0, x ′(t+ 0 ) = x ′ 0, (E) where h can be changed sign on [t0,∞) , by using the equivalence transformation, we establish an associated impulsive differential equation wit...

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...