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 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 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 Some Further Results on Oscillations for Neutral Delay Differential Equations with Variable Coefficients

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Fatima N. Ahmed ◽  
Rokiah Rozita Ahmad ◽  
Ummul Khair Salma Din ◽  
Mohd Salmi Md Noorani
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Variable Coefficients ◽  
Oscillatory Behaviour ◽  
Neutral Delay ◽  
Neutral Equations ◽  
First Order ◽  
All Solutions ◽  
Neutral Delay Differential Equations ◽  
Delay Differential

We study the oscillatory behaviour of all solutions of first-order neutral equations with variable coefficients. The obtained results extend and improve some of the well-known results in the literature. Some examples are given to show the evidence of our new results.

scholarly journals Oscillation of Nonlinear First Order Neutral Differential Equations

2007 ◽  
Vol 4 (3) ◽  
pp. 485-490
Author(s):  
Baghdad Science Journal
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Integral Conditions ◽  
Neutral Delay ◽  
Neutral Differential Equations ◽  
First Order ◽  
All Solutions ◽  
Neutral Delay Differential Equations ◽  
Delay Differential

In this paper, the author established some new integral conditions for the oscillation of all solutions of nonlinear first order neutral delay differential equations. Examples are inserted to illustrate the results.

An oscillation criteria for third order neutral delay differential equations

2010 ◽  
Vol 16 (2) ◽  
Author(s):  
Zhenlai Han ◽  
Tongxing Li ◽  
Shurong Sun ◽  
Chenghui Zhang
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Neutral Delay ◽  
Third Order ◽  
Oscillation Criteria ◽  
Neutral Delay Differential Equations ◽  
Delay Differential

On nonexistence of Kneser solutions of third-order neutral delay differential equations

2019 ◽  
Vol 88 ◽  
pp. 193-200 ◽  
Author(s):  
J. Džurina ◽  
S.R. Grace ◽  
I. Jadlovská
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Neutral Delay ◽  
Third Order ◽  
Neutral Delay Differential Equations ◽  
Delay Differential

Stability of third order neutral delay differential equations

2019 ◽  
Author(s):  
Alexander Domoshnitsky ◽  
Irina Volinsky ◽  
Shai Levi ◽  
Shirel Shemesh
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Neutral Delay ◽  
Third Order ◽  
Neutral Delay Differential Equations ◽  
Delay Differential

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 Asymptotic properties of the spectrum of neutral delay differential equations

2009 ◽  
Vol 24 (3) ◽  
pp. 361-372 ◽  
Author(s):  
Y.N. Kyrychko ◽  
K.B. Blyuss ◽  
P. Hövel ◽  
E. Schöll
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Asymptotic Properties ◽  
Neutral Delay ◽  
Neutral Delay Differential Equations ◽  
Delay Differential
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