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In this paper, the oscillation criteria for solutions of the neutral delay differential equation (NDDE) ${(y (t) - p (t) y (t - τ))}^{(n)} + α Q (t) G (y (t - σ)) = f (t)$ has been studied where $p (t) = 1$ or $p (t) \leq 0$ , $α = \pm 1$ , $Q \in C ([0, \infty), R^{+})$ , $f \in C ([0, \infty), R)$ , $G \in C (R, R)$ . This work improves and generalizes some recent results and answer some questions that are raised in [1].

Oscillation of solutions of some higher order linear differential equations.

Xu, Hong-Yan, Cao, Ting-Bin (2009)

Electronic Journal of Qualitative Theory of Differential Equations [electronic only]

Oscillation of solutions of the delay differential equation $y^{(2 n)} (t) + \sum_{i = 1}^{m} p_{i} (t) f_{j} (y [h_{i} (t)]) = 0$ , $n \geq 1$

Pavol Marušiak (1974)

Časopis pro pěstování matematiky

Oscillation of solutions to delay differential equations with positiv and negative coefficients.

Elabbasy, El M., Hegazi, A.S., Saker, S.H. (2000)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Oscillation of solutions to impulsive dynamic equations on time scales.

Li, Qiaoluan, Guo, Fang (2009)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Oscillation of solutions to neutral delay differential equations

Ireneusz Kubiaczyk, Samir H. Saker (2002)

Mathematica Slovaca

Oscillation of solutions to odd-order nonlinear neutral functional differential equations.

Li, Tongxing, Thandapani, Ethiraju (2011)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Oscillation of solutions to second order linear differential equations.

Seman, Jan (2004)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Oscillation of the Euler differential equation with delay

Mustafa R. S. Kulenović (1995)

Czechoslovak Mathematical Journal

Oscillation of the solution to a singular differential equation.

Kurepa, Alexandra, Weithers, Hugh (1999)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Oscillation of the solutions of a class of impulsive differential equations with a deviating argument.

Bainov, D.D., Dimitrova, Margarita B., Dishliev, Angel B. (1998)

Journal of Applied Mathematics and Stochastic Analysis

Oscillation of the solutions of neutral impulsive differential-difference equations of first order.

Dimitrova, M.B., Mishev, D. (2005)

Electronic Journal of Qualitative Theory of Differential Equations [electronic only]

Oscillation of the third order Euler differential equation with delay

Blanka Baculíková, Jozef Džurina (2014)

Mathematica Bohemica

In the paper we offer criteria for oscillation of the third order Euler differential equation with delay $y^{'''} (t) + \frac{k^{2}}{t^{3}} y (c t) = 0 .$ 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.

Oscillation of third order differential equation with damping term

Miroslav Bartušek, Zuzana Došlá (2015)

Czechoslovak Mathematical Journal

We study asymptotic and oscillatory properties of solutions to the third order differential equation with a damping term $x^{'''} (t) + q (t) x^{'} (t) + r (t) {| x |}^{λ} (t) sgn x (t) = 0, t \geq 0 .$ We give conditions under which every solution of the equation above is either oscillatory or tends to zero. In case $λ \leq 1$ and if the corresponding second order differential equation $h^{''} + q (t) h = 0$ is oscillatory, we also study Kneser solutions vanishing at infinity and the existence of oscillatory solutions.

Oscillation of third order functional differential equations with delay.

Candan, Tuncay, Dahiya, Rajbir S. (2003)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Oscillation of third-order functional differential equations.

Baculikova, B., Dzurina, J. (2010)

Electronic Journal of Qualitative Theory of Differential Equations [electronic only]

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