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20 results on '"superlinear neutral term"'

2. OSCILLATION CRITERIA FOR NON-CANONICAL SECOND-ORDER NONLINEAR DELAY DIFFERENCE EQUATIONS WITH A SUPERLINEAR NEUTRAL TERM.

Author

VIDHYAA, KUMAR S., THANDAPANI, ETHIRAJU, ALZABUT, JEHAD, and OZBEKLER, ABDULLAH

Abstract

We obtain oscillation conditions for non-canonical second-order nonlinear delay difference equations with a superlinear neutral term. To cope with non-canonical types of equations, we propose new oscillation criteria for the main equation when the neutral coefficient does not satisfy any of the conditions that call it to either converge to 0 or ∞. Our approach differs from others in that we first turn into the non-canonical equation to a canonical form and as a result, we only require one condition to weed out non-oscillatory solutions in order to induce oscillation. The conclusions made here are new and have been condensed significantly from those found in the literature. For the sake of confirmation, we provide examples that cannot be included in earlier works. [ABSTRACT FROM AUTHOR]

Published
2023
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3. Asymptotic behavior of semi-canonical third-order delay differential equations with a superlinear neutral term.

Author

Prabaharan, Natarajan, Thandapani, Ethiraju, and Tunç, Ercan

Subjects
DELAY differential equations, EQUATIONS, INTEGRALS
Abstract

This paper deals with the asymptotic behavior of solutions to a class of semicanonical third-order delay differential equations with a superlinear neutral term. First, we transform the semi-canonical equation into canonical type and then by applying a Riccati type transformation and integral conditions, we obtain some new sufficient conditions ensuring that every solution of the studied equation either oscillates or converges to zero asymptotically. The results are illustrated via two examples. [ABSTRACT FROM AUTHOR]

Published
2023

4. Oscillatory behavior of even-order functional differential equations with a superlinear neutral term.

Author

Dharuman, C., Prabaharan, N., Thandapani, E., and Tunç, E.

Subjects
FUNCTIONAL differential equations, DIFFERENTIAL equations
Abstract

The authors establish some new oscillation criteria for a class of even-order functional differential equations with a superlinear neutral term using comparison methods and integral conditions. The results obtained are complement and improve a number of existing ones in the literature. An example is provided to illustrate the main results. [ABSTRACT FROM AUTHOR]

Published
2023

5. On the Asymptotic Behavior of Noncanonical Third-Order Emden–Fowler Delay Differential Equations with a Superlinear Neutral Term.

Author

Liu, Qingmin, Grace, Said R., Jadlovská, Irena, Tunç, Ercan, and Li, Tongxing

Subjects
*DELAY differential equations, *DIFFERENTIAL equations
Abstract

The present paper is concerned with the asymptotic behavior of solutions to a class of noncanonical third-order Emden–Fowler delay differential equations with a superlinear neutral term. Using a Riccati-type transformation as well as integral criteria, we establish some new sufficient conditions guaranteeing that every solution of the equation considered either oscillates or converges to zero asymptotically. The results are illustrated with two examples. [ABSTRACT FROM AUTHOR]

Published
2022
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6. Oscillation theorems for higher order dynamic equations with superlinear neutral term

Author

Said R. Grace, Jehad Alzabut, and Kamaleldin Abodayeh

Subjects
oscillation criteria, superlinear neutral term, higher order dynamic equations, Mathematics, QA1-939
Abstract

In this paper, several oscillation criteria for a class of higher order dynamic equations with superlinear neutral term are established. The proposed results provide a unified platform that adequately covers both discrete and continuous equations and further sufficiently comments on oscillatory behavior of more general class of equations than the ones reported in the literature. We conclude the paper by demonstrating illustrative examples.

Published
2021
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9. On the Asymptotic Behavior of Noncanonical Third-Order Emden–Fowler Delay Differential Equations with a Superlinear Neutral Term

Author

Qingmin Liu, Said R. Grace, Irena Jadlovská, Ercan Tunç, and Tongxing Li

Subjects
oscillation, asymptotic behavior, third-order, noncanonical Emden–Fowler differential equation, superlinear neutral term, delayed argument, Mathematics, QA1-939
Abstract

The present paper is concerned with the asymptotic behavior of solutions to a class of noncanonical third-order Emden–Fowler delay differential equations with a superlinear neutral term. Using a Riccati-type transformation as well as integral criteria, we establish some new sufficient conditions guaranteeing that every solution of the equation considered either oscillates or converges to zero asymptotically. The results are illustrated with two examples.

Published
2022
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10. Oscillation criteria for second-order differential equations with superlinear neutral term.

Author

Bohner, Martin, Sudha, Balakrishnan, Tangavelu, Krishnan, and Thandapani, Ethiraju

Subjects
*FUNCTIONAL differential equations, *DIFFERENTIAL equations, *NONLINEAR differential equations, *OSCILLATIONS, *INTEGRAL inequalities
Abstract

In this paper, some sufficient conditions for the oscillation of all solutions of a secondorder nonlinear neutral differential equation with superlinear neutral term are obtained. By means of an inequality technique and an integral averaging method, some new oscillation criteria are presented which extend and complement those reported in the literature. [ABSTRACT FROM AUTHOR]

Published
2019

11. Oscillation theorems for higher order dynamic equations with superlinear neutral term

Author

Jehad Alzabut, Kamaleldin Abodayeh, and Said R. Grace

Subjects
Class (set theory), Oscillation, General Mathematics, lcsh:Mathematics, Applied mathematics, Order (group theory), oscillation criteria, higher order dynamic equations, lcsh:QA1-939, Dynamic equation, superlinear neutral term, Term (time), Mathematics
Abstract

In this paper, several oscillation criteria for a class of higher order dynamic equations with superlinear neutral term are established. The proposed results provide a unified platform that adequately covers both discrete and continuous equations and further sufficiently comments on oscillatory behavior of more general class of equations than the ones reported in the literature. We conclude the paper by demonstrating illustrative examples.

Published
2021

13. Oscillation of second order nonlinear difference equations with super-linear neutral term

Abstract

In this paper, the authors establish some new conditions for the oscillation of second order nonlinear difference equation of the form$$\Delta\left(a_n \Delta\left(y_n+p_n y_{n-k}^\alpha\right)\right)+q_n y_{n+1-\ell}^\beta=0,$$where $\alpha>1$ and $\beta$ are ratio of odd positive integers. Examples are provided to illustrate the importance of the main results.

Published
2019

14. Oscillation of second order nonlinear difference equations with super-linear neutral term

Abstract

In this paper, the authors establish some new conditions for the oscillation of second order nonlinear difference equation of the form$$\Delta\left(a_n \Delta\left(y_n+p_n y_{n-k}^\alpha\right)\right)+q_n y_{n+1-\ell}^\beta=0,$$where $\alpha>1$ and $\beta$ are ratio of odd positive integers. Examples are provided to illustrate the importance of the main results.

Published
2019

15. Oscillation of solutions of neutral differential equations with a superlinear neutral term

Author

Lin, Xiaoyan and Tang, X.H.

Subjects
*DIFFERENTIAL equations, *BESSEL functions, *CALCULUS, *ADJOINT differential equations
Abstract

Abstract: The oscillatory behavior of solutions of the neutral differential equations with a superlinear neutral term is studied in the case when . Two almost “sharp” oscillatory and non-oscillatory criteria are obtained. [Copyright &y& Elsevier]

Published
2007
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16. Oscillation of solutions of neutral difference equations with a nonlinear neutral term

Author

Lin, Xiaoyan

Subjects
*OSCILLATING chemical reactions, *NONLINEAR statistical models, *SOLUTIONS (Pharmacy), *DIFFERENCE equations, *MATHEMATICS
Abstract

Abstract: The oscillatory behavior of solutions of the neutral difference equations with nonlinear neutral term,is studied in the case when a ≠ 1. A necessary and sufficient oscillatory conditions for the case 0 < a < 1 and an almost “sharp” oscillatory and nonoscillatory criteria for the case a > 1 are obtained. [Copyright &y& Elsevier]

Published
2006
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17. Oscillation criteria for nonlinear difference equations with superlinear neutral term

Abstract

In this paper, the authors obtain sufficient conditions for the oscillation of all solutions of the equation$$\Delta\left(a_n \Delta\left(x_n+p_n x_{n-k}^\alpha\right)\right)+q_n x_{n+1-l}^\beta=0$$where $\alpha \geq 1$ and $\beta>0$ are ratio of odd positive integers, and $\left\{a_n\right\},\left\{p_n\right\}$ and $\left\{q_n\right\}$ are real positive sequences. Examples are provided to illustrate the importance of the main results.

Published
2017

18. Oscillation criteria for nonlinear difference equations with superlinear neutral term

Abstract

In this paper, the authors obtain sufficient conditions for the oscillation of all solutions of the equation$$\Delta\left(a_n \Delta\left(x_n+p_n x_{n-k}^\alpha\right)\right)+q_n x_{n+1-l}^\beta=0$$where $\alpha \geq 1$ and $\beta>0$ are ratio of odd positive integers, and $\left\{a_n\right\},\left\{p_n\right\}$ and $\left\{q_n\right\}$ are real positive sequences. Examples are provided to illustrate the importance of the main results.

Published
2017

19. Oscillation of solutions of neutral differential equations with a superlinear neutral term

Author

Xianhua Tang and Xiaoyan Lin

Subjects
Superlinear neutral term, Oscillation, First-order neutral differential equation, Differential equation, Applied Mathematics, Mathematical analysis, Neutral differential equations, Quotient, Mathematical physics, Mathematics
Abstract

The oscillatory behavior of solutions of the neutral differential equations with a superlinear neutral term[x(t)− px α (t −τ)] 0 +q(t)Y mj=1 |x(t −σ j )| β j sign[x(t −σ 1 )] = 0, t ≥ t 0 ,is studied in the case when α > 1. Two almost “sharp” oscillatory and non-oscillatory criteria are obtained.c 2007 Published by Elsevier Ltd Keywords: First-order neutral differential equation; Superlinear neutral term; Oscillation 1. IntroductionConsider the first-order neutral differential equation with a nonlinear neutral term[x(t)− px α (t −τ)] 0 +q(t)Y mj=1 |x(t −σ j )| β j sign[x(t −σ 1 )] = 0, t ≥ t 0 , (1.1)where p,τ ∈ (0,∞),α is a quotient of odd positive integers, σ j ∈ [0,∞),β j ∈ (0,∞), j = 1,2,...,m,q ∈C([t 0 ,∞),[0,∞)). When m = 1, Eq. (1.1) reduces to[x(t)− px α (t −τ)] 0 +q(t)|x(t −σ)| β−1 x(t −σ) = 0, t ≥ t 0 , (1.2)where σ = σ 1 ∈ [0,∞),β = β 1 ∈ (0,∞). When α = β = 1, Eq. (1.2) further reduces to a linear neutral differentialequation[x(t)− px(t −τ)] 0 +q(t)x(t −σ) = 0, t ≥ t

Published
2007

20. Oscillation of solutions of neutral difference equations with a nonlinear neutral term

Author

Xiaoyan Lin

Subjects
Neutral difference equation, Superlinear neutral term, Oscillation, Mathematical analysis, Term (time), Nonlinear system, Computational Mathematics, Computational Theory and Mathematics, Modeling and Simulation, Modelling and Simulation, Sublinear neutral term, Nonoscillation, Mathematics
Abstract

The oscillatory behavior of solutions of the neutral difference equations with nonlinear neutral term,Δ(xn−pnxn−τα)+qnxn−σβ=0,n≥n0is studied in the case when a ≠ 1. A necessary and sufficient oscillatory conditions for the case 0 < a < 1 and an almost “sharp” oscillatory and nonoscillatory criteria for the case a > 1 are obtained.

Published
2006
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