Displaying similar documents to “Oscillation of a second order delay differential equations”

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.

Oscillation results for second order nonlinear differential equations

Jozef Džurina, Dáša Lacková (2004)

Open Mathematics

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In this paper, the authors present some new results for the oscillation of the second order nonlinear neutral differential equations of the form r t ψ x t x t + p t x τ t ' ' + q t f x σ t = 0 . Easily verifiable criteria are obtained that are also new for differential equations without neutral term i.e. for p(t)≡0.

Oscillation of the third order Euler differential equation with delay

Blanka Baculíková, Jozef Džurina (2014)

Mathematica Bohemica

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In the paper we offer criteria for oscillation of the third order Euler differential equation with delay y ' ' ' ( t ) + k 2 t 3 y ( c t ) = 0 . We provide detail analysis of the properties of this equation, we fill the gap in the oscillation theory and provide necessary and sufficient conditions for oscillation of equation considered.

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.