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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.

Oscillation of solutions of non-linear neutral delay differential equations of higher order for p ( t ) = ± 1

Radhanath N. Rath, Laxmi N. Padhy, Niyati Misra (2004)

Archivum Mathematicum

In this paper, the oscillation criteria for solutions of the neutral delay differential equation (NDDE) y ( t ) - p ( t ) y ( t - τ ) ( n ) + α Q ( t ) G y ( t - σ ) = f ( t ) has been studied where p ( t ) = 1 or p ( t ) ≤ 0 , α = ± 1 , Q ∈ C [ 0 , ∞ ) , R + , f ∈ C ( [ 0 , ∞ ) , R ) , G ∈ C ( R , R ) . This work improves and generalizes some recent results and answer some questions that are raised in [1].

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