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

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
B. Baculikova ◽  
J. Dzurina

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.

Symmetry ◽  
2020 ◽  
Vol 12 (8) ◽  
pp. 1248 ◽  
Author(s):  
Omar Bazighifan ◽  
Osama Moaaz ◽  
Rami Ahmad El-Nabulsi ◽  
Ali Muhib

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.


2021 ◽  
Vol 40 (2) ◽  
pp. 505-523
Author(s):  
Osama Moaaz ◽  
Clemente Cesarano

In this work, we study the oscillation of the fourth order neutral differential equations with delay argument. By means of generalized Riccati transformation technique, we obtain new oscillation criteria for oscillation of this equation. An example is given to clarify the main results in this paper.


Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 650
Author(s):  
Ahmed AlGhamdi ◽  
Clemente Cesarano ◽  
Barakah Almarri ◽  
Omar Bazighifan

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.


2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Omar Bazighifan ◽  
Alanoud Almutairi

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.


Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 552 ◽  
Author(s):  
Omar Bazighifan ◽  
Mihai Postolache

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.


Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 656 ◽  
Author(s):  
Omar Bazighifan ◽  
Thabet Abdeljawad

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.


2021 ◽  
Vol 11 (1) ◽  
pp. 425
Author(s):  
Osama Moaaz ◽  
Ioannis Dassios ◽  
Haifa Bin Jebreen ◽  
Ali Muhib

The objective of this study was to improve existing oscillation criteria for delay differential equations (DDEs) of the fourth order by establishing new criteria for the nonexistence of so-called Kneser solutions. The new criteria are characterized by taking into account the effect of delay argument. All previous relevant results have neglected the effect of the delay argument, so our results substantially improve the well-known results reported in the literature. The effectiveness of our new criteria is illustrated via an example.


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