scholarly journals New Oscillation Criteria for Advanced Differential Equations of Fourth Order

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 728 ◽  
Author(s):  
Omar Bazighifan ◽  
Hijaz Ahmad ◽  
Shao-Wen Yao
Keyword(s):  
Differential Equations ◽  
Fourth Order ◽  
Second Order ◽  
Delay Equations ◽  
Riccati Transformation ◽  
Oscillation Criteria ◽  
Delayed Arguments

The main objective of this paper is to establish new oscillation results of solutions to a class of fourth-order advanced differential equations with delayed arguments. The key idea of our approach is to use the Riccati transformation and the theory of comparison with first and second-order delay equations. Four examples are provided to illustrate the main results.

scholarly journals Improved Approach for Studying Oscillatory Properties of Fourth-Order Advanced Differential Equations with p-Laplacian Like Operator

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 656 ◽  
Author(s):  
Omar Bazighifan ◽  
Thabet Abdeljawad
Keyword(s):  
Differential Equations ◽  
Fourth Order ◽  
Delay Equations ◽  
Riccati Transformation ◽  
Oscillation Criteria ◽  
First Order ◽  
Oscillatory Properties

This paper aims to study the oscillatory properties of fourth-order advanced differential equations with p-Laplacian like operator. By using the technique of Riccati transformation and the theory of comparison with first-order delay equations, we will establish some new oscillation criteria for this equation. Some examples are considered to illustrate the main results.

scholarly journals Some New Oscillation Criteria for Second Order Neutral Differential Equations with Delayed Arguments

Mathematics ◽  
2019 ◽  
Vol 7 (7) ◽  
pp. 619 ◽  
Author(s):  
Omar Bazighifan ◽  
Clemente Cesarano
Keyword(s):  
Differential Equations ◽  
Second Order ◽  
Riccati Transformation ◽  
Oscillation Criteria ◽  
Neutral Differential Equations ◽  
Delayed Arguments

In this paper, we study the oscillation of second-order neutral differential equations with delayed arguments. Some new oscillatory criteria are obtained by a Riccati transformation. To illustrate the importance of the results, one example is also given.

scholarly journals Oscillation Theorems for Advanced Differential Equations with p-Laplacian Like Operators

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 821 ◽  
Author(s):  
Omar Bazighifan ◽  
Poom Kumam
Keyword(s):  
Differential Equations ◽  
Second Order ◽  
Delay Equations ◽  
Riccati Transformation ◽  
Even Order ◽  
Oscillation Theorems

The main objective of this paper is to establish new oscillation results of solutions to a class of even-order advanced differential equations with a p-Laplacian like operator. The key idea of our approach is to use the Riccati transformation and the theory of comparison with first and second-order delay equations. Some examples are provided to illustrate the main results.

scholarly journals Delay Differential Equations of Fourth-Order: Oscillation and Asymptotic Properties of Solutions

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2015
Author(s):  
Omar Bazighifan ◽  
Maryam Al-Kandari ◽  
Khalil S. Al-Ghafri ◽  
F. Ghanim ◽  
Sameh Askar ◽  
...  
Keyword(s):  
Differential Equations ◽  
Canonical Form ◽  
Fourth Order ◽  
Delay Differential Equations ◽  
Essential Role ◽  
Asymptotic Properties ◽  
Comparison Method ◽  
Riccati Transformation ◽  
Oscillation Criteria ◽  
Delay Differential

In this work, by using the comparison method and Riccati transformation, we obtain some oscillation criteria of solutions of delay differential equations of fourth-order in canonical form. These criteria complement those results in the literature. We give two examples to illustrate the main results. Symmetry plays an essential role in determining the correct methods for solutions to differential equations.

Oscillation Criteria for Second Order Nonlinear Delay Equations

1973 ◽  
Vol 16 (1) ◽  
pp. 49-56 ◽  
Author(s):  
Lynn Erbe
Keyword(s):  
Differential Equations ◽  
Nonlinear Differential Equations ◽  
Second Order ◽  
Delay Equations ◽  
Retarded Argument ◽  
Oscillation Criteria ◽  
Image Position ◽  
Nonlinear Delay

It is the purpose of this paper to establish oscillation criteria for second order nonlinear differential equations with retarded argument. Specifically, we consider the equation1.1where f ∊ C[0, + ∞) x R2, g ∊ C[0, + ∞), and1.2We shall restrict attention to solutions of (1.1) which exist on some ray [T, + ∞). A solution of (1.1) is called oscillatory if it has no largest zero.

scholarly journals On the Oscillation Criteria for Fourth-Order p -Laplacian Differential Equations with Middle Term

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Dandan Yang ◽  
Chuanzhi Bai
Keyword(s):  
Differential Equations ◽  
Fourth Order ◽  
Second Order ◽  
Middle Term ◽  
Oscillation Criteria ◽  
Second Order Differential Equations ◽  
Oscillatory Properties

In this paper, we study the oscillatory properties of the solutions of a class of fourth-order p -Laplacian differential equations with middle term. The new oscillation criteria obtained by using the theory of comparison with first- and second-order differential equations and a refinement of the Riccati transformations. The results in this paper improve and generalize the corresponding results in the literatures. Three examples are provided to illustrate our results.

scholarly journals Interval Oscillation Criteria for Super-Half-Linear Impulsive Differential Equations with Delay

2012 ◽  
Vol 2012 ◽  
pp. 1-22 ◽  
Author(s):  
Zhonghai Guo ◽  
Xiaoliang Zhou ◽  
Wu-Sheng Wang
Keyword(s):  
Differential Equations ◽  
Impulsive Differential Equations ◽  
Second Order ◽  
Riccati Transformation ◽  
Oscillation Criteria ◽  
Nonnegative Constant ◽  
Interval Oscillation ◽  
Equations With Delay

We study the following second-order super-half-linear impulsive differential equations with delay[r(t)φγ(x′(t))]′+p(t)φγ(x(t-σ))+q(t)f(x(t-σ))=e(t),t≠τk,x(t+)=akx(t),x′(t+)=bkx′(t),t=τk, wheret≥t0∈ℝ,φ*(u)=|u|*-1u,σis a nonnegative constant,{τk}denotes the impulsive moments sequence withτ1<τ2<⋯<τk<⋯,lim k→∞τk=∞, andτk+1-τk>σ. By some classical inequalities, Riccati transformation, and two classes of functions, we give several interval oscillation criteria which generalize and improve some known results. Moreover, we also give two examples to illustrate the effectiveness and nonemptiness of our results.

Oscillation of Second Order Half-Linear Differential Equations with Damping

2003 ◽  
Vol 10 (4) ◽  
pp. 785-797
Author(s):  
Qigui Yang ◽  
Sui Sun Cheng
Keyword(s):  
Differential Equations ◽  
Second Order ◽  
Linear Differential Equations ◽  
Riccati Transformation ◽  
Averaging Technique ◽  
Oscillation Criteria ◽  
Generalized Riccati Transformation ◽  
Linear Differential

Abstract This paper is concerned with a class of second order half-linear damped differential equations. Using the generalized Riccati transformation and the averaging technique, new oscillation criteria are obtained which are either extensions of or complementary to a number of the existing results.

scholarly journals New oscillation criteria for second-order neutral differential equations with distributed deviating arguments

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Osama Moaaz ◽  
Choonkil Park ◽  
Elmetwally M. Elabbasy ◽  
Waed Muhsin
Keyword(s):  
Differential Equations ◽  
Second Order ◽  
The Other ◽  
Riccati Transformation ◽  
Transformation Technique ◽  
Deviating Arguments ◽  
Neutral Differential Equations ◽  
Second Order Differential Equations ◽  
Continuous Delay ◽  
New Criteria

AbstractIn this work, we create new oscillation conditions for solutions of second-order differential equations with continuous delay. The new criteria were created based on Riccati transformation technique and comparison principles. Furthermore, we obtain iterative criteria that can be applied even when the other criteria fail. The results obtained in this paper improve and extend the relevant previous results as illustrated by examples.

scholarly journals Emden–Fowler-type neutral differential equations: oscillatory properties of solutions

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Omar Bazighifan ◽  
Alanoud Almutairi
Keyword(s):  
Differential Equations ◽  
Fourth Order ◽  
Delay Differential Equations ◽  
Comparison Method ◽  
Riccati Transformation ◽  
Neutral Differential Equations ◽  
Neutral Term ◽  
Delay Differential ◽  
Oscillatory Properties

AbstractIn this paper, we study the oscillation of a class of fourth-order Emden–Fowler delay differential equations with neutral term. Using the Riccati transformation and comparison method, we establish several new oscillation conditions. These new conditions complement a number of results in the literature. We give examples to illustrate our main results.

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