Oscillation of unstable second order neutral differential equations with mixed argument

Jozef Džurina; Viktor Pirč

Displaying similar documents to “Oscillation of unstable second order neutral differential equations with mixed argument”

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.

Oscillatory behaviour of a higher order nonlinear neutral delay type functional differential equation with oscillating coefficients

Yaşar Bolat, Ömer Akin (2005)

Czechoslovak Mathematical Journal

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In this paper we are concerned with the oscillation of solutions of a certain more general higher order nonlinear neutral type functional differential equation with oscillating coefficients. We obtain two sufficient criteria for oscillatory behaviour of its solutions.

Oscillation theorems for certain even order neutral differential equations

Qi Gui Yang, Sui-Sun Cheng (2007)

Archivum Mathematicum

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This paper is concerned with a class of even order nonlinear differential equations of the form $\frac{d}{d t} (| {(x (t) + p (t) x (τ (t)))}^{(n - 1)} |^{α - 1} {(x (t) + p (t) x (τ (t)))}^{(n - 1)}) + F (t, x (g (t))) = 0,$ where $n$ is even and $t \geq t_{0}$ . By using the generalized Riccati transformation and the averaging technique, new oscillation criteria are obtained which are either extensions of or complementary to a number of existing results. Our results are more general and sharper than some previous results even for second order equations.