Displaying similar documents to “Classifications and existence of nonoscillatory solutions of second order nonlinear neutral differential equations”

Oscillatory behaviour of solutions of forced neutral differential equations

N. Parhi, P. K. Mohanty (1996)

Annales Polonici Mathematici

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Sufficient conditions are obtained for oscillation of all solutions of a class of forced nth order linear and nonlinear neutral delay differential equations. Also, asymptotic behaviour of nonoscillatory solutions of a class of forced first order neutral equations is studied.

Linearized comparison criteria for a nonlinear neutral differential equation

Xinping Guan, Sui Sun Cheng (1996)

Annales Polonici Mathematici

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A class of nonlinear neutral differential equations with variable coefficients and delays is considered. Conditions for the existence of eventually positive solutions are obtained which extend some of the criteria existing in the literature. In particular, a linearized comparison theorem is obtained which establishes a connection between our nonlinear equations and a class of linear neutral equations with constant coefficients.

Interval Oscillation for Second Order Nonlinear Differential Equations with a Damping Term

Hassan, Taher S. (2008)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: 34C10, 34C15. It is the purpose of this paper to give oscillation criteria for the second order nonlinear differential equation with a damping term (a(t) y′(t))′ + p(t)y′(t) + q(t) |y(t)| α−1 y(t) = 0, t ≥ t0, where α ≥ 1, a ∈ C1([t0,∞);(0,∞)) and p,q ∈ C([t0,∞);R). Our results here are different, generalize and improve some known results for oscillation of second order nonlinear differential equations that are different from most...

Oscillation conditions for first-order nonlinear advanced differential equations

Özkan Öcalan, Nurten Kiliç (2023)

Commentationes Mathematicae Universitatis Carolinae

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Our purpose is to analyze a first order nonlinear differential equation with advanced arguments. Then, some sufficient conditions for the oscillatory solutions of this equation are presented. Our results essentially improve two conditions in the paper “Oscillation tests for nonlinear differential equations with several nonmonotone advanced arguments” by N. Kilıç, Ö. Öcalan and U. M. Özkan. Also we give an example to illustrate our results.

Oscillation of nonlinear neutral delay differential equations of second order

Ireneusz Kubiaczyk, Samir H. Saker (2002)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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Oscillation criteria, extended Kamenev and Philos-type oscillation theorems for the nonlinear second order neutral delay differential equation with and without the forced term are given. These results extend and improve the well known results of Grammatikopoulos et. al., Graef et. al., Tanaka for the nonlinear neutral case and the recent results of Dzurina and Mihalikova for the neutral linear case. Some examples are considered to illustrate our main results.

Oscillation of Nonlinear Neutral Delay Differential Equations

Elabbasy, E. M., Hassan, T. S. (2008)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: 34K15, 34C10. In this paper, we study the oscillatory behavior of first order nonlinear neutral delay differential equation (x(t) − q(t) x(t − σ(t))) ′ +f(t,x( t − τ(t))) = 0, where σ, τ ∈ C([t0,∞),(0,∞)), q О C([t0,∞), [0,∞)) and f ∈ C([t0,∞) ×R,R). The obtained results extended and improve several of the well known previously results in the literature. Our results are illustrated with an example.

An improved oscillation theorem for nonlinear differential equations of advanced type

Nurten Kiliç, Özkan Öcalan, Mustafa Kemal Yildiz (2024)

Archivum Mathematicum

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This paper deals with the oscillatory solutions of the first order nonlinear advanced differential equation. The aim of the present paper is to obtain an oscillation condition for this equation. This result is new and improves and correlates many of the well-known oscillation criteria that were in the literature. Finally, an example is given to illustrate the main result.