scholarly journals Weighted differential inequality and oscillatory properties of fourth order differential equations

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Aigerim Kalybay ◽  
Ryskul Oinarov ◽  
Yaudat Sultanaev
Keyword(s):  
Differential Equations ◽  
Fourth Order ◽  
Differential Inequality ◽  
Boundary Behavior ◽  
Oscillatory Properties

AbstractIn this paper, we investigate the oscillatory properties of two fourth order differential equations in dependence on boundary behavior of its coefficients at infinity. These properties are established based on two-sided estimates of the least constant of a certain weighted differential inequality.

scholarly journals Differential inequality and non-oscillation of fourth order differential equation

2021 ◽  
Vol 104 (4) ◽  
pp. 103-109
Author(s):  
A.A. Kalybay ◽  
◽  
A.O. Baiarystanov ◽  
Keyword(s):  
Differential Equations ◽  
Variational Method ◽  
Fourth Order ◽  
Differential Inequality ◽  
Order Differential Equation ◽  
Boundary Behavior ◽  
Power Functions ◽  
Hardy Type ◽  
Fourth Order Differential Equation ◽  
Oscillatory Properties

The oscillatory theory of fourth order differential equations has not yet been developed well enough. The results are known only for the case when the coefficients of differential equations are power functions. This fact can be explained by the absence of simple effective methods for studying such higher order equations. In this paper, the authors investigate the oscillatory properties of a class of fourth order differential equations by the variational method. The presented variational method allows to consider any arbitrary functions as coefficients, and our main results depend on their boundary behavior in neighborhoods of zero and infinity. Moreover, this variational method is based on the validity of a certain weighted differential inequality of Hardy type, which is of independent interest. The authors of the article also find two-sided estimates of the least constant for this inequality, which are especially important for their applications to the main results on the oscillatory properties of these differential equations.

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.

scholarly journals Improved Conditions for Oscillation of Functional Nonlinear Differential Equations

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 552 ◽  
Author(s):  
Omar Bazighifan ◽  
Mihai Postolache
Keyword(s):  
Differential Equations ◽  
Fourth Order ◽  
Delay Differential Equations ◽  
Nonlinear Differential Equations ◽  
Oscillation Criteria ◽  
Delay Differential ◽  
Oscillatory Properties

The aim of this work is to study oscillatory properties of a class of fourth-order delay differential equations. New oscillation criteria are obtained by using generalized Riccati transformations. This new theorem complements and improves a number of results reported in the literature. Some 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 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 Symmetry and Its Importance in the Oscillation of Solutions of Differential Equations

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 650
Author(s):  
Ahmed AlGhamdi ◽  
Clemente Cesarano ◽  
Barakah Almarri ◽  
Omar Bazighifan
Keyword(s):  
Differential Equations ◽  
Fourth Order ◽  
First Order ◽  
Main Equation ◽  
Engineering Physics ◽  
Equations With Delay ◽  
Oscillation Of Solutions ◽  
Oscillatory Properties

Oscillation and symmetry play an important role in many applications such as engineering, physics, medicine, and vibration in flight. The purpose of this article is to explore the oscillation of fourth-order differential equations with delay arguments. New Kamenev-type oscillatory properties are established, which are based on a suitable Riccati method to reduce the main equation into a first-order inequality. Our new results extend and simplify existing results in the previous studies. Examples are presented in order to clarify the main results.

scholarly journals Oscillation of fourth-order strongly noncanonical differential equations with delay argument

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
B. Baculikova ◽  
J. Dzurina
Keyword(s):  
Differential Equations ◽  
Fourth Order ◽  
Nonoscillatory Solutions ◽  
Delay Argument ◽  
Equations With Delay ◽  
Oscillatory Properties

Abstract The aim of this paper is to study oscillatory properties of the fourth-order strongly noncanonical equation of the form $$ \bigl(r_{3}(t) \bigl(r_{2}(t) \bigl(r_{1}(t)y'(t) \bigr)' \bigr)' \bigr)'+p(t)y \bigl( \tau (t) \bigr)=0, $$ ( r 3 ( t ) ( r 2 ( t ) ( r 1 ( t ) y ′ ( t ) ) ′ ) ′ ) ′ + p ( t ) y ( τ ( t ) ) = 0 , where $\int ^{\infty }\frac{1}{r_{i}(s)}\,\mathrm {d}{s}<\infty $ ∫ ∞ 1 r i ( s ) d s < ∞ , $i=1,2,3$ i = 1 , 2 , 3 . Reducing possible classes of the nonoscillatory solutions, new oscillatory criteria are established.

scholarly journals New Criteria for Oscillation of Half-Linear Differential Equations with p-Laplacian-Like Operators

Mathematics ◽  
2021 ◽  
Vol 9 (20) ◽  
pp. 2584
Author(s):  
Omar Bazighifan ◽  
F. Ghanim ◽  
Jan Awrejcewicz ◽  
Khalil S. Al-Ghafri ◽  
Maryam Al-Kandari
Keyword(s):  
Differential Equations ◽  
Fourth Order ◽  
Delay Differential Equations ◽  
Comparison Method ◽  
Linear Differential Equations ◽  
Riccati Transformation ◽  
Linear Differential ◽  
Delay Differential ◽  
New Criteria ◽  
Oscillatory Properties

In this paper, new oscillatory properties for fourth-order delay differential equations with p-Laplacian-like operators are established, using the Riccati transformation and comparison method. Moreover, our results are an extension and complement to previous results in the literature. We provide some examples to examine the applicability of our results.

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.

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