Displaying similar documents to “Conditions for oscillation of a neutral differential equation.”

On the asymptotic behavior of a class of third order nonlinear neutral differential equations

Blanka Baculíková, Jozef Džurina (2010)

Open Mathematics

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The objective of this paper is to study asymptotic properties of the third-order neutral differential equation a t x t + p t x σ t ' ' γ ' + q t f x τ t = 0 , t ⩾ t 0 . E . We will establish two kinds of sufficient conditions which ensure that either all nonoscillatory solutions of (E) converge to zero or all solutions of (E) are oscillatory. Some examples are considered to illustrate the main results.

Oscillation of second order neutral delay differential equations

J. Džurina, D. Hudáková (2009)

Mathematica Bohemica

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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.