An oscillation criterion of linear delay differential equations

An Oscillation Criterion for Nonlinear Third-order Differential Equations

Sufficient conditions for oscillation of a certain class of nonlinear third-order differential equations are found. In this paper we considear a nonlinear third-order differential equation of the form y′′′ + q(t)y′ = f(t, y, y′, y′′) (1) where (i) q, q′ ∈ C ( (a,∞) ) for some a with 0 < a < ∞, (ii) f ∈ C ( (a,∞)×R3 ) , t ∈ (a,∞), and y1, y2, y3 ∈ R and f(t, y1, y2, y3)y1 < 0 for all t ∈ (a,∞) a...

Oscillation of Solutions of Linear Differential Equations

In this note we study the zeros of solutions of differential equations of the form u + pu = 0. A criterion for oscillation is found, and some sharper forms of the Sturm comparison theorem are given. §1. Number of zeros. Consider the linear differential equation u′′(x) + p(x) u(x) = 0 , where p(x) = 1 (1− x) , (1) on the interval −1 < x < 1. Two independent solutions are

New oscillation criterion for delay differential equations with non-monotone arguments

Impulsive Stabilization of Linear Delay Differential Equations

The paper is concerned with stabilization of a scalar delay differention equation ẋ(t)− m ∑ k=1 Ak(t)x[hk(t)] = 0, t ≥ 0, x(ξ) = φ(ξ), ξ < 0, by introducing impulses in certain moments of time x(τj) = Bjx(τj − 0), j = 1, 2, . . . . Explicit stability results are presented both for the equation with positive coefficients and for the equation with Ak being of arbitrary sign. Supported by Israel M...

Oscillation of Nonlinear Neutral Delay Differential Equations of Second Order

Oscillation criteria, extended Kamenev and Philos-type oscillation theorems for the nonlinear second order neutral delay differential equation with and without the forced term are given. These results extend and improve the well known results of Grammatikopoulos et. al., Graef et. al., Tanaka for the nonlinear neutral case and the recent results of Dzurina and Mihalikova for the neutral linear ...