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

Displaying similar documents to “Existence of nonoscillatory solutions to third order neutral type difference equations with delay and advanced arguments”

On the oscillation of solutions of third order linear difference equations of neutral type

Anna Andruch-Sobiło, Małgorzata Migda (2005)

Mathematica Bohemica

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In this note we consider the third order linear difference equations of neutral type $Δ^{3} [x (n) - p (n) x (σ (n))] + δ q (n) x (τ (n)) = 0, n \in N (n_{0}), (E)$ where $δ = \pm 1$ , $p, q N (n_{0}) \to ℝ_{+};$ $σ, τ N (n_{0}) \to ℕ$ , ${lim}_{n \to \infty} σ (n) = lim_{n \to \infty} τ (n) = \infty .$ We examine the following two cases: $\begin{matrix} {0 < p (n) & \leq 1, σ (n) = n + k, τ (n) = n + l}, {p (n) & > 1, σ (n) = n - k, τ (n) = n - l}, \end{matrix}$ where $k$ , $l$ are positive integers and we obtain sufficient conditions under which all solutions of the above equations are oscillatory.

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...

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 criteria for third order nonlinear delay dynamic equations on time scales

Zhenlai Han, Tongxing Li, Shurong Sun, Fengjuan Cao (2010)

Annales Polonici Mathematici

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By means of Riccati transformation technique, we establish some new oscillation criteria for third-order nonlinear delay dynamic equations ${({(x^{Δ Δ} (t))}^{γ})}^{Δ} + p (t) x^{γ} (τ (t)) = 0$ on a time scale ; here γ > 0 is a quotient of odd positive integers and p a real-valued positive rd-continuous function defined on . Our results not only extend and improve the results of T. S. Hassan [Math. Comput. Modelling 49 (2009)] but also unify the results on oscillation of third-order delay differential equations and third-order delay...

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.

Comparison and oscillation results for delay difference equations with oscillating coefficients.

Yan, Weiping, Yan, Jurang (1996)

International Journal of Mathematics and Mathematical Sciences

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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 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 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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On property (B) of higher order delay differential equations

Blanka Baculíková, Jozef Džurina (2012)

Archivum Mathematicum

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In this paper we offer criteria for property (B) and additional asymptotic behavior of solutions of the $n$ -th order delay differential equations ${(r (t) {[x^{(n - 1)} (t)]}^{γ})}^{'} = q (t) f (x (τ (t))) .$ Obtained results essentially use new comparison theorems, that permit to reduce the problem of the oscillation of the n-th order equation to the the oscillation of a set of certain the first order equations. So that established comparison principles essentially simplify the examination of studied equations. Both cases $\int^{\infty} r^{- 1 / γ} (t) t = \infty$ and $\int^{\infty} r^{- 1 / γ} (t) t < \infty$ are discussed. ...

Oscillation Criteria of Second-Order Quasi-Linear Neutral Delay Difference Equations

Thandapani, E., Pandian, S., Revathi, T. (2010)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: 39A10. The oscillatory and nonoscillatory behaviour of solutions of the second order quasi linear neutral delay difference equation Δ(an | Δ(xn+pnxn-τ)|α-1 Δ(xn+pnxn-τ) + qnf(xn-σ)g(Δxn) = 0 where n ∈ N(n0), α > 0, τ, σ are fixed non negative integers, {an}, {pn}, {qn} are real sequences and f and g real valued continuous functions are studied. Our results generalize and improve some known results of neutral delay difference equations. ...