Displaying similar documents to “Oscillation theorems for neutral differential equations of higher order”

On unstable neutral differential equations of the second order

Jozef Džurina (2002)

Czechoslovak Mathematical Journal

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The aim of this paper is to present sufficient conditions for all bounded solutions of the second order neutral differential equation ( x ( t ) - p x ( t - τ ) ) ' ' - q ( t ) x ( σ ( t ) ) = 0 to be oscillatory and to improve some existing results. The main results are based on the comparison principles.

Oscillation of a higher order neutral differential equation with a sub-linear delay term and positive and negative coefficients

Julio G. Dix, Dillip Kumar Ghose, Radhanath Rath (2009)

Mathematica Bohemica

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We obtain sufficient conditions for every solution of the differential equation [ y ( t ) - p ( t ) y ( r ( t ) ) ] ( n ) + v ( t ) G ( y ( g ( t ) ) ) - u ( t ) H ( y ( h ( t ) ) ) = f ( t ) to oscillate or to tend to zero as t approaches infinity. In particular, we extend the results of Karpuz, Rath and Padhy (2008) to the case when G has sub-linear growth at infinity. Our results also apply to the neutral equation [ y ( t ) - p ( t ) y ( r ( t ) ) ] ( n ) + q ( t ) G ( y ( g ( t ) ) ) = f ( t ) when q ( t ) has sign changes. Both bounded and unbounded solutions are consideted here; thus some known results are expanded.

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.