Linearized oscillation theory for a nonlinear delay impulsive equation

Linearized oscillation theory for a nonlinear equation with a distributed delay

We obtain linearized oscillation theorems for the equation with distributed delays ẋ(t)+ m ∑ k=1 rk(t) ∫ t −∞ fk(x(s)) ds Rk(t, s) = 0. (1) The results are applied to logistic, Lasota–Wazewska and Nicholson’s blowflies equations with a distributed delay. In addition, the “Mean Value Theorem” is proved which claims that a solution of (1) also satisfies the linear equation with a variable concent...

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...

Linearized Comparison Criteria for a First Order Nonlinear Neutral Delay Difference Equation

On Oscillation of a Second Order Impulsive Linear Delay Differential Equation