scholarly journals Oscillation and Asymptotic Properties of Differential Equations of Third-Order

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 192
Author(s):  
R. Elayaraja ◽  
V. Ganesan ◽  
Omar Bazighifan ◽  
Clemente Cesarano
Keyword(s):  
Differential Equations ◽  
Asymptotic Properties ◽  
Neutral Delay ◽  
Third Order ◽  
Riccati Technique ◽  
Neutral Delay Differential Equations ◽  
The Subject ◽  
Delay Differential ◽  
New Criteria ◽  
Noncanonical Operator

The main purpose of this study is aimed at developing new criteria of the iterative nature to test the asymptotic and oscillation of nonlinear neutral delay differential equations of third order with noncanonical operator (a(ι)[(b(ι)x(ι)+p(ι)x(ι−τ)′)′]β)′+∫cdq(ι,μ)xβ(σ(ι,μ))dμ=0, where ι≥ι0 and w(ι):=x(ι)+p(ι)x(ι−τ). New oscillation results are established by using the generalized Riccati technique under the assumption of ∫ι0ιa−1/β(s)ds<∫ι0ι1b(s)ds=∞asι→∞. Our new results complement the related contributions to the subject. An example is given to prove the significance of new theorem.

scholarly journals Oscillatory Properties of Third-Order Neutral Delay Differential Equations with Noncanonical Operators

Mathematics ◽  
2019 ◽  
Vol 7 (12) ◽  
pp. 1177 ◽  
Author(s):  
George E. Chatzarakis ◽  
Jozef Džurina ◽  
Irena Jadlovská
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Asymptotic Properties ◽  
Differential Inequalities ◽  
Neutral Delay ◽  
Third Order ◽  
All Solutions ◽  
Neutral Delay Differential Equations ◽  
Delay Differential ◽  
New Criteria

In the paper, we study the oscillatory and asymptotic properties of solutions to a class of third-order linear neutral delay differential equations with noncanonical operators. Via the application of comparison principles with associated first and second-order delay differential inequalities, we offer new criteria for the oscillation of all solutions to a given differential equation. Our technique essentially simplifies the process of investigation and reduces the number of conditions required in previously known results. The strength of the newly obtained results is illustrated on the Euler type equations.

scholarly journals Third-Order Neutral Delay Differential Equations: New Iterative Criteria for Oscillation

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Osama Moaaz ◽  
Emad E. Mahmoud ◽  
Wedad R. Alharbi
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Iterative Technique ◽  
Neutral Delay ◽  
Third Order ◽  
Neutral Delay Differential Equations ◽  
Delay Differential ◽  
New Criterion ◽  
New Criteria

This study is aimed at developing new criteria of the iterative nature to test the oscillation of neutral delay differential equations of third order. First, we obtain a new criterion for the nonexistence of the so-called Kneser solutions, using an iterative technique. Further, we use several methods to obtain different criteria, so that a larger area of the models can be covered. The examples provided strongly support the importance of the new results.

scholarly journals Neutral Delay Differential Equations: Oscillation Conditions for the Solutions

Symmetry ◽  
2021 ◽  
Vol 13 (1) ◽  
pp. 101
Author(s):  
Omar Bazighifan ◽  
Hammad Alotaibi ◽  
Abd Allaah A. Mousa
Keyword(s):  
Differential Equations ◽  
Fourth Order ◽  
Asymptotic Properties ◽  
Neutral Delay ◽  
Neutral Differential Equations ◽  
First Order ◽  
Theoretical Support ◽  
Neutral Delay Differential Equations ◽  
Delay Differential ◽  
New Criteria

The purpose of this article is to explore the asymptotic properties for a class of fourth-order neutral differential equations. Based on a comparison with the differential inequality of the first-order, we have provided new oscillation conditions for the solutions of fourth-order neutral differential equations. The obtained results can be used to develop and provide theoretical support for and to further develop the study of oscillation for a class of fourth-order neutral differential equations. Finally, we provide an illustrated example to demonstrate the effectiveness of our new criteria.

scholarly journals On the Asymptotic Properties of Nonlinear Third-Order Neutral Delay Differential Equations with Distributed Deviating Arguments

2016 ◽  
Vol 2016 ◽  
pp. 1-5
Author(s):  
Youliang Fu ◽  
Yazhou Tian ◽  
Cuimei Jiang ◽  
Tongxing Li
Keyword(s):  
Differential Equation ◽  
Delay Differential Equations ◽  
Asymptotic Properties ◽  
Neutral Delay ◽  
Third Order ◽  
Deviating Arguments ◽  
Neutral Delay Differential Equation ◽  
Distributed Deviating Arguments ◽  
Neutral Delay Differential Equations ◽  
Delay Differential

This paper is concerned with the asymptotic properties of solutions to a third-order nonlinear neutral delay differential equation with distributed deviating arguments. Several new theorems are obtained which ensure that every solution to this equation either is oscillatory or tends to zero. Two illustrative examples are included.

scholarly journals On a class of third order neutral delay differential equations with piecewise constant argument

1994 ◽  
Vol 17 (1) ◽  
pp. 113-117 ◽  
Author(s):  
Garyfalos Papaschinopoulos
Keyword(s):  
Asymptotic Stability ◽  
Differential Equations ◽  
Delay Differential Equations ◽  
Neutral Delay ◽  
Third Order ◽  
Piecewise Constant ◽  
Piecewise Constant Argument ◽  
Neutral Delay Differential Equations ◽  
Delay Differential ◽  
Constant Argument

In this paper we study existence, uniqueness and asymptotic stability of the solutions of a class of third order neutral delay differential equations with piecewise constant argument.

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