scholarly journals Oscillation theorems for second order advanced neutral differential equations

2011 ◽  
Vol 48 (1) ◽  
pp. 61-71 ◽  
Author(s):  
Jozef Džurina
Keyword(s):  
Differential Equations ◽  
Order Equation ◽  
Second Order ◽  
Comparison Theorems ◽  
Comparison Principles ◽  
Neutral Differential Equations ◽  
First Order ◽  
Oscillation Theorems

Abstract The aim of this paper is to study the oscillation of the second order advanced neutral differential equations . (E) Obtained results are based on the new comparison theorems that enable us to reduce problem of the oscillation of the second order equation to the the oscillation of the first order equations. Obtained comparison principles essentially simplify the examination of the studied equations.

scholarly journals Oscillation theorems for third order neutral differential equations

2012 ◽  
Vol 28 (2) ◽  
pp. 199-206
Author(s):  
BLANKA BACULIKOVA ◽  
◽  
J. DZURINA ◽  
Keyword(s):  
Differential Equations ◽  
Asymptotic Properties ◽  
Order Equation ◽  
Comparison Theorems ◽  
Third Order ◽  
Comparison Principles ◽  
Neutral Differential Equations ◽  
First Order ◽  
The Third ◽  
Oscillation Theorems

The aim of this paper is to study the asymptotic properties and the oscillation of the third order neutral differential equations ... Obtained results are based on the new comparison theorems, that permit to reduce the problem of the oscillation of the third order equation to the oscillation of the couple of the first order equation. Obtained comparison principles essentially simplify the examination of the studied equations.

Oscillation theorems for second-order superlinear neutral differential equations

2013 ◽  
Vol 63 (1) ◽  
Author(s):  
Blanka Baculíková ◽  
Tongxing Li ◽  
Jozef Džurina
Keyword(s):  
Differential Equations ◽  
Second Order ◽  
Comparison Principles ◽  
Neutral Differential Equations ◽  
Oscillation Theorems

AbstractThe purpose of this paper is to investigate the oscillation of the second-order neutral differential equations of the form (E)$$ (r(t)|z'(t)|^{\alpha - 1} z'(t))' + q(t)|x(\sigma (t))|^{\alpha - 1} x(\sigma (t)) = 0, $$ where z(t) = x(t) + p(t)x(τ(t)). The obtained comparison principles essentially simplify the examination of the studied equations. Further, our results extend and improve the results in the literature.

scholarly journals Non-Linear Neutral Differential Equations with Damping: Oscillation of Solutions

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 285
Author(s):  
Saad Althobati ◽  
Jehad Alzabut ◽  
Omar Bazighifan
Keyword(s):  
Differential Equations ◽  
Oscillatory Behavior ◽  
Order Equation ◽  
Second Order ◽  
Riccati Technique ◽  
Neutral Equations ◽  
Neutral Differential Equations ◽  
Main Equation ◽  
Non Linear ◽  
Even Order

The oscillation of non-linear neutral equations contributes to many applications, such as torsional oscillations, which have been observed during earthquakes. These oscillations are generally caused by the asymmetry of the structures. The objective of this work is to establish new oscillation criteria for a class of nonlinear even-order differential equations with damping. We employ different approach based on using Riccati technique to reduce the main equation into a second order equation and then comparing with a second order equation whose oscillatory behavior is known. The new conditions complement several results in the literature. Furthermore, examining the validity of the proposed criteria has been demonstrated via particular examples.

scholarly journals Oscillation theorems of solution of second-order neutral differential equations

2021 ◽  
Vol 6 (11) ◽  
pp. 12771-12779
Author(s):  
Ali Muhib ◽  
◽  
Hammad Alotaibi ◽  
Omar Bazighifan ◽  
Kamsing Nonlaopon ◽  
...  
Keyword(s):  
Differential Equations ◽  
Functional Differential Equations ◽  
Second Order ◽  
Neutral Functional Differential Equations ◽  
Neutral Differential Equations ◽  
Theoretical Support ◽  
Functional Differential ◽  
Oscillation Theorems ◽  
New Criteria ◽  
Oscillation Of Solutions

<abstract><p>In this paper, we aim to explore the oscillation of solutions for a class of second-order neutral functional differential equations. We propose new criteria to ensure that all obtained solutions are oscillatory. The obtained results can be used to develop and provide theoretical support for and further develop the oscillation study for a class of second-order neutral differential equations. Finally, an illustrated example is given to demonstrate the effectiveness of our new criteria.</p></abstract>

scholarly journals Oscillation of even-order neutral differential equations via comparison principles

2014 ◽  
Vol 30 (3) ◽  
pp. 293-300
Author(s):  
J. DZURINA ◽  
◽  
B. BACULIKOVA ◽  
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Delay Differential Equations ◽  
Order Differential Equation ◽  
Higher Order ◽  
Comparison Principles ◽  
Neutral Differential Equations ◽  
First Order ◽  
Even Order ◽  
Delay Differential

In the paper we offer oscillation criteria for even-order neutral differential equations, where z(t) = x(t) + p(t)x(τ(t)). Establishing a generalization of Philos and Staikos lemma, we introduce new comparison principles for reducing the examination of the properties of the higher order differential equation onto oscillation of the first order delay differential equations. The results obtained are easily verifiable.

scholarly journals New Comparison Theorems for the Nth Order Neutral Differential Equations with Delay Inequalities

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 454 ◽  
Author(s):  
Osama Moaaz ◽  
Shigeru Furuichi ◽  
Ali Muhib
Keyword(s):  
Differential Equations ◽  
Higher Order ◽  
Comparison Theorems ◽  
Differential Inequalities ◽  
Neutral Differential Equations ◽  
First Order ◽  
A New Technique ◽  
Equations With Delay ◽  
Higher Order Differential Equations ◽  
First Order Differential Equations

In this work, we present a new technique for the oscillatory properties of solutions of higher-order differential equations. We set new sufficient criteria for oscillation via comparison with higher-order differential inequalities. Moreover, we use the comparison with first-order differential equations. Finally, we provide an example to illustrate the importance of the results.

scholarly journals Oscillation results for second-order neutral differential equations of mixed type

2011 ◽  
Vol 48 (1) ◽  
pp. 101-116 ◽  
Author(s):  
Tongxing Li ◽  
Blanka Baculíková ◽  
Jozef Džurina
Keyword(s):  
Differential Equations ◽  
Mixed Type ◽  
Second Order ◽  
Order Linear ◽  
Neutral Differential Equations ◽  
Equations Of Mixed Type ◽  
Oscillation Theorems

Abstract Some oscillation theorems are established for the second-order linear neutral differential equations of mixed type Several examples are also provided to illustrate the main results.

scholarly journals Improved Oscillation Criteria for 2nd-Order Neutral Differential Equations with Distributed Deviating Arguments

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 849
Author(s):  
Osama Moaaz ◽  
Rami Ahmad El-Nabulsi ◽  
Waad Muhsin ◽  
Omar Bazighifan
Keyword(s):  
Differential Equations ◽  
Sufficient Conditions ◽  
Second Order ◽  
Deviating Arguments ◽  
Oscillation Criteria ◽  
Comparison Principles ◽  
Neutral Differential Equations ◽  
Distributed Deviating Arguments ◽  
Oscillation Of Solutions

In this study, we establish new sufficient conditions for oscillation of solutions of second-order neutral differential equations with distributed deviating arguments. By employing a refinement of the Riccati transformations and comparison principles, we obtain new oscillation criteria that complement and improve some results reported in the literature. Examples are provided to illustrate the main results.

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