Displaying similar documents to “Oscillation of the third order Euler differential equation with delay”

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.

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 second order delay differential equations

Jozef Džurina (1997)

Archivum Mathematicum

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In this paper, we study the oscillatory behavior of the solutions of the delay differential equation of the form 1 r ( t ) y ' ( t ) ' + p ( t ) y ( τ ( t ) ) = 0 . The obtained results are applied to n-th order delay differential equation with quasi-derivatives of the form L n u ( t ) + p ( t ) u ( τ ( t ) ) = 0 .