scholarly journals Oscillation Conditions for Certain Fourth-Order Non-Linear Neutral Differential Equation

Symmetry ◽  
2020 ◽  
Vol 12 (7) ◽  
pp. 1096 ◽  
Author(s):  
Ioannis Dassios ◽  
Omar Bazighifan
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Fourth Order ◽  
Neutral Differential Equation ◽  
Riccati Technique ◽  
Oscillation Criteria ◽  
Neutral Differential Equations ◽  
Non Linear ◽  
The Right ◽  
Oscillation Of Solutions

In this work, new conditions were obtained for the oscillation of solutions of fourth-order non-linear neutral differential equations (NDEs) using the Riccati technique. These oscillation criteria complement and improve those of Chatzarakis et al. (2019). Symmetry plays an important role in determining the right way to study these equation. An example is given to illustrate our theory.

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.

scholarly journals Some New Oscillation Results for Fourth-Order Neutral Differential Equations with Delay Argument

Symmetry ◽  
2020 ◽  
Vol 12 (8) ◽  
pp. 1248 ◽  
Author(s):  
Omar Bazighifan ◽  
Osama Moaaz ◽  
Rami Ahmad El-Nabulsi ◽  
Ali Muhib
Keyword(s):  
Differential Equations ◽  
Fourth Order ◽  
Oscillation Criteria ◽  
Neutral Differential Equations ◽  
Delay Argument ◽  
The Right ◽  
Equations With Delay ◽  
Oscillatory Properties

The aim of this paper is to study the oscillatory properties of 4th-order neutral differential equations. We obtain some oscillation criteria for the equation by the theory of comparison. The obtained results improve well-known oscillation results in the literate. Symmetry plays an important role in determining the right way to study these equation. An example to illustrate the results is given.

scholarly journals Second-Order Neutral Differential Equations: Improved Criteria for Testing the Oscillation

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Osama Moaaz ◽  
Ali Muhib ◽  
Saud Owyed ◽  
Emad E. Mahmoud ◽  
Aml Abdelnaser
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Second Order ◽  
Neutral Differential Equation ◽  
Neutral Differential Equations ◽  
New Criteria ◽  
Oscillation Of Solutions

The main purpose of this study is to establish new improved conditions for testing the oscillation of solutions of second-order neutral differential equation r l u ′ l γ ′ + q l x β σ l = 0 , where l ≥ l 0 and u l ≔ x l + p x ϱ l . By optimizing the commonly used relationship x > 1 − p u , we obtain new criteria that give sharper results for oscillation than the previous related results. Moreover, we obtain criteria of an iterative nature. Our new results are illustrated by an example.

Oscillation results for second-order mixed neutral differential equations with distributed deviating arguments

2016 ◽  
Vol 66 (3) ◽  
Author(s):  
Chenghui Zhang ◽  
Blanka Baculíková ◽  
Jozef Džurina ◽  
Tongxing Li
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Second Order ◽  
Neutral Differential Equation ◽  
Deviating Arguments ◽  
Oscillation Criteria ◽  
Neutral Differential Equations ◽  
Distributed Deviating Arguments ◽  
All Solutions

AbstractWe obtain some oscillation criteria for all solutions to a second-order mixed neutral differential equation with distributed deviating arguments. The results presented improve those reported in the literature.

scholarly journals New Oscillation Criteria for Neutral Delay Differential Equations of Fourth-Order

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1277
Author(s):  
Saeed Althubiti ◽  
Omar Bazighifan ◽  
Hammad Alotaibi ◽  
Jan Awrejcewicz
Keyword(s):  
Differential Equations ◽  
Fourth Order ◽  
Delay Differential Equations ◽  
Neutral Delay ◽  
Riccati Technique ◽  
Deviating Arguments ◽  
Oscillation Criteria ◽  
Neutral Delay Differential Equations ◽  
Delay Differential ◽  
Oscillation Of Solutions

New oscillatory properties for the oscillation of solutions to a class of fourth-order delay differential equations with several deviating arguments are established, which extend and generalize related results in previous studies. Some oscillation results are established by using the Riccati technique under the case of canonical coefficients. The symmetry plays an important and fundamental role in the study of the oscillation of solutions of the equations. Examples are given to prove the significance of the new theorems.

scholarly journals New Oscillation Results for Second-Order Neutral Differential Equations with Deviating Arguments

Symmetry ◽  
2020 ◽  
Vol 12 (12) ◽  
pp. 1937
Author(s):  
Yakun Wang ◽  
Fanwei Meng
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Delay Differential Equation ◽  
Second Order ◽  
Deviating Arguments ◽  
Oscillation Criteria ◽  
Neutral Differential Equations ◽  
First Order ◽  
Delay Differential ◽  
The Right

In this paper, we focus on the second-order neutral differential equations with deviating arguments which are under the canonical condition. New oscillation criteria are established, which are based on a first-order delay differential equation and generalized Riccati transformations. The idea of symmetry is a useful tool, not only guiding us in the right way to study this function but also simplifies our proof. Our results are generalizations of some previous results and we provide an example to illustrate the main results.

scholarly journals On oscillation of second-order noncanonical neutral differential equations

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Ali Muhib
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Second Order ◽  
Neutral Differential Equation ◽  
Oscillation Criteria ◽  
Neutral Differential Equations

AbstractIn the present work, we study the second-order neutral differential equation and formulate new oscillation criteria for this equation. Our conditions differ from the earlier ones. Also, our results are expansions and generalizations of some previous results. Examples to illustrate the main results are included.

Oscillation of certain third-order quasilinear neutral differential equations

2014 ◽  
Vol 64 (1) ◽  
Author(s):  
Linlin Yang ◽  
Zhiting Xu
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Nonlinear Differential Equations ◽  
Neutral Differential Equation ◽  
Third Order ◽  
Oscillation Criteria ◽  
Neutral Differential Equations ◽  
The Third ◽  
Positive Integers ◽  
Type Oscillation

AbstractIn this paper, new oscillation criteria for the third-order quasilinear neutral differential equation $$\left( {a\left( t \right)\left( {z''\left( t \right)} \right)^\gamma } \right)^\prime + q\left( t \right)x^\gamma \left( {\tau \left( t \right)} \right) = 0, t \geqslant t_0 ,$$ are established, where z(t) = x(t) + p(t)x(δ(t)), and γ is a ratio of odd positive integers. Those results extend the oscillation criteria due to Sun [SUN, Y. G.: New Kamenev-type oscillation criteria for second-order nonlinear differential equations with damping, J. Math. Anal. Appl. 291 (2004) 341–351] to the equation, and complement the existing results in literature. Two examples are provided to illustrate the relevance of our main theorems.

scholarly journals Oscillation of higher-order half-linear neutral differential equations

2013 ◽  
Vol 46 (1) ◽  
Author(s):  
Shuhong Tang ◽  
Tongxing Li ◽  
E. Thandapani
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Higher Order ◽  
Neutral Differential Equation ◽  
Oscillation Criteria ◽  
Neutral Differential Equations

AbstractIn this paper, we establish some new oscillation criteria for the higher-order half-linear neutral differential equation

scholarly journals A Philos-Type Oscillation Criteria for Fourth-Order Neutral Differential Equations

Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 379 ◽  
Author(s):  
Omar Bazighifan ◽  
Clemente Cesarano
Keyword(s):  
Differential Equations ◽  
Fourth Order ◽  
Averaging Method ◽  
Sufficient Conditions ◽  
Neutral Differential Equations ◽  
Future Developments ◽  
Correct Direction ◽  
The Right ◽  
Type Oscillation ◽  
Oscillation Of Solutions

Some sufficient conditions are established for the oscillation of fourth order neutral differential equations of the form r t z ‴ t α ′ + q t x β σ t = 0 , where z t : = x t + p t x τ t . By using the technique of Riccati transformation and integral averaging method, we get conditions to ensure oscillation of solutions of this equation. Symmetry ideas are often invisible in these studies, but they help us decide the right way to study them, and to show us the correct direction for future developments. Moreover, the importance of the obtained conditions is illustrated via some examples.

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