scholarly journals New Aspects for Non-Existence of Kneser Solutions of Neutral Differential Equations with Odd-Order

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 494 ◽  
Author(s):  
Osama Moaaz ◽  
Dumitru Baleanu ◽  
Ali Muhib
Keyword(s):  
Differential Equations ◽  
Asymptotic Properties ◽  
Sufficient Conditions ◽  
Neutral Differential Equations ◽  
Odd Order ◽  
All Solutions

Some new oscillatory and asymptotic properties of solutions of neutral differential equations with odd-order are established. Through the new results, we give sufficient conditions for the oscillation of all solutions of the studied equations, and this is an improvement of the relevant results. The efficiency of the obtained criteria is illustrated via example.

scholarly journals Oscillatory behavior of solutions of certain third order mixed neutral differential equations

2013 ◽  
Vol 44 (1) ◽  
pp. 99-112 ◽  
Author(s):  
Ethiraj Thandapani ◽  
Renu Rama
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Asymptotic Properties ◽  
Sufficient Conditions ◽  
Continuous Functions ◽  
Oscillatory Behavior ◽  
Third Order ◽  
Neutral Differential Equations ◽  
All Solutions ◽  
Positive Integers

The objective of this paper is to study the oscillatory and asymptotic properties of third order mixed neutral differential equation of the form $$ (a(t) [x(t) + b(t) x(t - \tau_{1}) + c(t) x(t + \tau_{2})]'')' + q(t) x^{\alpha}(t - \sigma_{1}) + p(t) x^{\beta}(t + \sigma_{2}) = 0 $$where $a(t), b(t), c(t), q(t)$ and $p(t)$ are positive continuous functions, $\alpha$ and $\beta$ are ratios of odd positive integers, $\tau_{1}, \tau_{2}, \sigma_{1}$ and $\sigma_{2}$ are positive constants. We establish some sufficient conditions which ensure that all solutions are either oscillatory or converge to zero. Some examples are provided to illustrate the main results.

scholarly journals New Results for Oscillation of Solutions of Odd-Order Neutral Differential Equations

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1095
Author(s):  
Clemente Cesarano ◽  
Osama Moaaz ◽  
Belgees Qaraad ◽  
Nawal A. Alshehri ◽  
Sayed K. Elagan ◽  
...  
Keyword(s):  
Differential Equations ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Oscillatory Behavior ◽  
Neutral Delay ◽  
Neutral Differential Equations ◽  
Odd Order ◽  
Future Prediction ◽  
Functional Differential ◽  
Delay Differential

Differential equations with delay arguments are one of the branches of functional differential equations which take into account the system’s past, allowing for more accurate and efficient future prediction. The symmetry of the equations in terms of positive and negative solutions plays a fundamental and important role in the study of oscillation. In this paper, we study the oscillatory behavior of a class of odd-order neutral delay differential equations. We establish new sufficient conditions for all solutions of such equations to be oscillatory. The obtained results improve, simplify and complement many existing results.

scholarly journals Oscillation and non-oscillation of some neutral differential equations of odd order

1992 ◽  
Vol 15 (3) ◽  
pp. 509-515 ◽  
Author(s):  
B. S. Lalli ◽  
B. G. Zhang
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Sufficient Conditions ◽  
Nonoscillatory Solution ◽  
Neutral Differential Equation ◽  
Neutral Differential Equations ◽  
Neutral Term ◽  
Odd Order ◽  
Existence Criterion ◽  
Oscillation Of Solutions

An existence criterion for nonoscillatory solution for an odd order neutral differential equation is provided. Some sufficient conditions are also given for the oscillation of solutions of somenth order equations with nonlinearity in the neutral term.

On oscillatory fourth order nonlinear neutral differential equations – III

2018 ◽  
Vol 68 (6) ◽  
pp. 1385-1396 ◽  
Author(s):  
Arun Kumar Tripathy ◽  
Rashmi Rekha Mohanta
Keyword(s):  
Differential Equations ◽  
Fourth Order ◽  
Functional Differential Equations ◽  
Neutral Type ◽  
Sufficient Conditions ◽  
Neutral Differential Equations ◽  
All Solutions ◽  
Functional Differential ◽  
T Tau

Abstract In this paper, several sufficient conditions for oscillation of all solutions of fourth order functional differential equations of neutral type of the form $$\begin{array}{} \displaystyle \bigl(r(t)(y(t)+p(t)y(t-\tau))''\bigr)''+q(t)G\bigl(y(t-\sigma)\bigr)=0 \end{array}$$ are studied under the assumption $$\begin{array}{} \displaystyle \int\limits^{\infty}_{0}\frac{t}{r(t)}{\rm d} t =\infty \end{array}$$

scholarly journals Oscillatory and asymptotic properties of higher-order quasilinear neutral differential equations

2021 ◽  
Vol 6 (10) ◽  
pp. 11124-11138
Author(s):  
Clemente Cesarano ◽  
◽  
Osama Moaaz ◽  
Belgees Qaraad ◽  
Ali Muhib ◽  
...  
Keyword(s):  
Differential Equations ◽  
Asymptotic Properties ◽  
Higher Order ◽  
Riccati Transformation ◽  
Oscillation Criteria ◽  
Neutral Differential Equations ◽  
Odd Order ◽  
Several Delays ◽  
New Criteria

<abstract><p>The objective of this paper is to study the oscillation criteria for odd-order neutral differential equations with several delays. We establish new oscillation criteria by using Riccati transformation. Our new criteria are interested in complementing and extending some results in the literature. An example is considered to illustrate our results.</p></abstract>

Improved oscillation criteria for even-order neutral differential equations

Analysis ◽  
2021 ◽  
Vol 0 (0) ◽  
Author(s):  
George E. Chatzarakis ◽  
Irena Jadlovská ◽  
Ercan Tunç
Keyword(s):  
Differential Equations ◽  
Sufficient Conditions ◽  
Future Research ◽  
Oscillation Criteria ◽  
Neutral Differential Equations ◽  
All Solutions ◽  
Even Order ◽  
Appl Math

Abstract New sufficient conditions for the oscillation of all solutions to a class of even-order differential equations with bounded and unbounded neutral coefficients are established, which refine, significantly simplify and generalize those in [T. Li and Y. V. Rogovchenko, Oscillation criteria for even-order neutral differential equations, Appl. Math. Lett. 61 2016, 35–41]. Examples are provided to illustrate the results and suggestions for future research are included.

scholarly journals On Oscillatory and Asymptotic Behavior of a Second-Order Nonlinear Damped Neutral Differential Equation

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Ercan Tunç ◽  
Said R. Grace
Keyword(s):  
Differential Equation ◽  
Asymptotic Behavior ◽  
Differential Equations ◽  
Asymptotic Properties ◽  
Sufficient Conditions ◽  
Second Order ◽  
Neutral Differential Equation ◽  
Neutral Differential Equations

This paper discusses oscillatory and asymptotic properties of solutions of a class of second-order nonlinear damped neutral differential equations. Some new sufficient conditions for any solution of the equation to be oscillatory or to converge to zero are given. The results obtained extend and improve some of the related results reported in the literature. The results are illustrated with examples.

scholarly journals Some further results on oscillation of neutral differential equations

1992 ◽  
Vol 46 (1) ◽  
pp. 149-157 ◽  
Author(s):  
Jianshe Yu ◽  
Zhicheng Wang
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Sufficient Conditions ◽  
Variable Coefficients ◽  
Neutral Differential Equation ◽  
Neutral Differential Equations ◽  
All Solutions ◽  
Image Position

We obtain new sufficient conditions for the oscillation of all solutions of the neutral differential equation with variable coefficientswhere P, Q, R ∈ C([t0, ∞), R+), r ∈ (0, ∞) and τ, σ ∈ [0, ∞). Our results improve several known results in papers by: Chuanxi and Ladas; Lalli and Zhang; Wei; Ruan.

scholarly journals Establishing New Criteria for Oscillation of Odd-Order Nonlinear Differential Equations

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 937
Author(s):  
Osama Moaaz ◽  
Jan Awrejcewicz ◽  
Ali Muhib
Keyword(s):  
Differential Equations ◽  
Nonlinear Differential Equations ◽  
Sufficient Conditions ◽  
Odd Order ◽  
All Solutions ◽  
New Criteria

By establishing new conditions for the non-existence of so-called Kneser solutions, we can generate sufficient conditions to ensure that all solutions of odd-order equations are oscillatory. Our results improve and expand the previous results in the literature.

scholarly journals Oscillation Criteria for Solutions of Neutral Differential Equations of Impulses Effect with Positive and Negative Coefficients

2020 ◽  
Vol 17 (2) ◽  
pp. 0537
Author(s):  
Aqeel Jaddoa et al.
Keyword(s):  
Differential Equations ◽  
Sufficient Conditions ◽  
Impulsive Conditions ◽  
Neutral Differential Equations ◽  
First Order ◽  
Positive And Negative Coefficients ◽  
Oscillation Property ◽  
All Solutions ◽  
Impulsive Neutral Differential Equations ◽  
Necessary And Sufficient

In this paper, some necessary and sufficient conditions are obtained to ensure the oscillatory of all solutions of the first order impulsive neutral differential equations. Also, some results in the references have been improved and generalized. New lemmas are established to demonstrate the oscillation property. Special impulsive conditions associated with neutral differential equation are submitted. Some examples are given to illustrate the obtained results.

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