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Oscillation of Nonlinear Neutral Delay Differential Equations

Elabbasy, E. M., Hassan, T. S. (2008)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 34K15, 34C10.In this paper, we study the oscillatory behavior of first order nonlinear neutral delay differential equation (x(t) − q(t) x(t − σ(t))) ′ +f(t,x( t − τ(t))) = 0, where σ, τ ∈ C([t0,∞),(0,∞)), q О C([t0,∞), [0,∞)) and f ∈ C([t0,∞) ×R,R). The obtained results extended and improve several of the well known previously results in the literature. Our results are illustrated with an example.

Oscillation of second order neutral delay differential equations

J. Džurina, D. Hudáková (2009)

Mathematica Bohemica

We establish some new oscillation criteria for the second order neutral delay differential equation [ r ( t ) | [ x ( t ) + p ( t ) x [ τ ( t ) ] ] ' | α - 1 [ x ( t ) + p ( t ) x [ τ ( t ) ] ] ' ] ' + q ( t ) f ( x [ σ ( t ) ] ) = 0 . The obtained results supplement those of Dzurina and Stavroulakis, Sun and Meng, Xu and Meng, Baculíková and Lacková. We also make a slight improvement of one assumption in the paper of Xu and Meng.

Oscillation of second-order linear delay differential equations

Ján Ohriska (2008)

Open Mathematics

The aim of this paper is to derive sufficient conditions for the linear delay differential equation (r(t)y′(t))′ + p(t)y(τ(t)) = 0 to be oscillatory by using a generalization of the Lagrange mean-value theorem, the Riccati differential inequality and the Sturm comparison theorem.

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