Oscillation criteria for third order nonlinear delay dynamic equations on time scales

Zhenlai Han; Tongxing Li; Shurong Sun; Fengjuan Cao

Displaying similar documents to “Oscillation criteria for third order nonlinear delay dynamic equations on time scales”

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.

Oscillation of nonlinear neutral delay differential equations with applications

Wan-Tong Li, S. H. Saker (2001)

Annales Polonici Mathematici

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We consider nonlinear neutral delay differential equations with variable coefficients. Finite and infinite integral conditions for oscillation are obtained. As an example, the neutral delay logistic differential equation is discussed.

Existence of nonoscillatory solutions to third order neutral type difference equations with delay and advanced arguments

Srinivasan Selvarangam, Sethurajan A. Rupadevi, Ethiraju Thandapani, Sandra Pinelas (2021)

Mathematica Bohemica

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In this paper, we present several sufficient conditions for the existence of nonoscillatory solutions to the following third order neutral type difference equation $Δ^{3} (x_{n} + a_{n} x_{n - l} + b_{n} x_{n + m}) + p_{n} x_{n - k} - q_{n} x_{n + r} = 0, n \geq n_{0}$ via Banach contraction principle. Examples are provided to illustrate the main results. The results obtained in this paper extend and complement some of the existing 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 delay differential equation with several positive and negative coefficients

E.M. Elabbasy, S.H. Saker (2003)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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Some sufficient conditions for oscillation of a first order nonautonomuous delay differential equation with several positive and negative coefficients are obtained.

On oscillation of a kind of integro-differential equation with delay

Binggen Zhang (1988)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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This note contains a criterion for the oscillation of solution of a kind of integro-differential equations with delay.

On oscillation of a kind of integro-differential equation with delay

Binggen Zhang (1988)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

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This note contains a criterion for the oscillation of solution of a kind of integro-differential equations with delay.

On the oscillation of second-order neutral delay differential equations.

Han, Zhenlai, Li, Tongxing, Sun, Shurong, Chen, Weisong (2010)

Advances in Difference Equations [electronic only]

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Oscillation of even-order neutral delay differential equations.

Li, Tongxing, Han, Zhenlai, Zhao, Ping, Sun, Shurong (2010)

Advances in Difference Equations [electronic only]

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Oscillation of delay differential equations

J. Džurina (1997)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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Our aim in this paper is to present the relationship between property (B) of the third order equation with delay argument y'''(t) - q(t)y(τ(t)) = 0 and the oscillation of the second order delay equation of the form y''(t) + p(t)y(τ(t)) = 0.

Oscillation criteria for second-order quasilinear neutral delay dynamic equations on time scales.

Sun, Yibing, Han, Zhenlai, Li, Tongxing, Zhang, Guangrong (2010)

Advances in Difference Equations [electronic only]

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Oscillation theorems for third order nonlinear delay difference equations

Kumar S. Vidhyaa, Chinnappa Dharuman, Ethiraju Thandapani, Sandra Pinelas (2019)

Mathematica Bohemica

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Sufficient conditions are obtained for the third order nonlinear delay difference equation of the form $Δ (a_{n} (Δ (b_{n} {(Δ y_{n})}^{α}))) + q_{n} f (y_{σ (n)}) = 0$ to have property $(A)$ or to be oscillatory. These conditions improve and complement many known results reported in the literature. Examples are provided to illustrate the importance of the main results.

Oscillation properties of second-order quasilinear difference equations with unbounded delay and advanced neutral terms

George E. Chatzarakis, Ponnuraj Dinakar, Srinivasan Selvarangam, Ethiraju Thandapani (2022)

Mathematica Bohemica

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We obtain some new sufficient conditions for the oscillation of the solutions of the second-order quasilinear difference equations with delay and advanced neutral terms. The results established in this paper are applicable to equations whose neutral coefficients are unbounded. Thus, the results obtained here are new and complement some known results reported in the literature. Examples are also given to illustrate the applicability and strength of the obtained conditions over the known...

Oscillation criteria for a class of second-order neutral delay dynamic equations of Emden-Fowler type.

Han, Zhenlai, Li, Tongxing, Sun, Shurong, Zhang, Chao, Han, Bangxian (2011)

Abstract and Applied Analysis

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On the existence of positive solutions of second order neutral difference equations

Wen-Xian Lin (2004)

Applicationes Mathematicae

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The neutral delay difference equations of second order with positive and negative coefficients $Δ ² (x ₙ + p ₙ x_{n - τ}) + q ₙ x_{n - σ} - r ₙ x_{n - λ} = 0$ , n = 0,1,2,... studied sufficient condition existence positive solution equation obtained

Oscillation of second-order neutral delay and mixed-type dynamic equations on time scales.

Şahıner, Y. (2006)

Advances in Difference Equations [electronic only]

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Oscillation criteria for second-order neutral delay dynamic equations with mixed nonlinearities.

Thandapani, Ethiraju, Piramanantham, Veeraraghavan, Pinelas, Sandra (2011)

Advances in Difference Equations [electronic only]

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On oscillatory nonlinear fourth-order difference equations with delays

Arun K. Tripathy (2018)

Mathematica Bohemica

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In this work, oscillatory behaviour of solutions of a class of fourth-order neutral functional difference equations of the form $Δ^{2} (r (n) Δ^{2} (y (n) + p (n) y (n - m))) + q (n) G (y (n - k)) = 0$ is studied under the assumption $\sum_{n = 0}^{\infty} \frac{n}{r (n)} < \infty .$ New oscillation criteria have been established which generalize some of the existing results in the literature.