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Keywords = Kneser-type criteria

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13 pages, 268 KB  
Article
Iterative Kneser-Type Criteria for Oscillation of Half-Linear Second-Order Advanced Dynamic Equations
by Taher S. Hassan, Bassant M. El-Matary, Ioan-Lucian Popa, Mouataz Billah Mesmouli, Ismoil Odinaev and Yousef Jawarneh
Mathematics 2025, 13(4), 635; https://doi.org/10.3390/math13040635 - 14 Feb 2025
Viewed by 716
Abstract
This work aims to develop new iterative Kneser-type criteria for determining the oscillatory behaviour of half-linear second-order advanced dynamic equations on arbitrary unbounded-above time scales T. The results extend and refine previously established criteria for these equations while also generalising classical criteria [...] Read more.
This work aims to develop new iterative Kneser-type criteria for determining the oscillatory behaviour of half-linear second-order advanced dynamic equations on arbitrary unbounded-above time scales T. The results extend and refine previously established criteria for these equations while also generalising classical criteria for corresponding ordinary dynamic equations. This study provides a broader and more flexible approach to analysing such systems by introducing iterative methods. Several examples are included to demonstrate the accuracy, usefulness, and adaptability. Full article
20 pages, 330 KB  
Article
Third-Order Neutral Differential Equations with Non-Canonical Forms: Novel Oscillation Theorems
by Barakah Almarri, Belal Batiha, Omar Bazighifan and Fahd Masood
Axioms 2024, 13(11), 755; https://doi.org/10.3390/axioms13110755 - 31 Oct 2024
Cited by 8 | Viewed by 1139
Abstract
This paper explores the asymptotic and oscillatory properties of a class of third-order neutral differential equations with multiple delays in a non-canonical form. The main objective is to simplify the non-canonical form by converting it to a canonical form, which reduces the complexity [...] Read more.
This paper explores the asymptotic and oscillatory properties of a class of third-order neutral differential equations with multiple delays in a non-canonical form. The main objective is to simplify the non-canonical form by converting it to a canonical form, which reduces the complexity of the possible cases of positive solutions and their derivatives from four cases in the non-canonical form to only two cases in the canonical form, which facilitates the process of inference and development of results. New criteria are provided that exclude the existence of positive solutions or Kneser-type solutions for this class of equations. New criteria that guarantee the oscillatory behavior of all solutions that satisfy the conditions imposed on the studied equation are also derived. This work makes a qualitative contribution to the development of previous studies in the field of neutral differential equations, as it provides new insights into the oscillatory behavior of neutral equations with multiple delays. To confirm the strength and effectiveness of the results, three examples are included that highlight the accuracy of the derived criteria and their practical applicability, which enhances the value of this research and expands the scope of its use in the field. Full article
(This article belongs to the Special Issue Difference, Functional, and Related Equations)
10 pages, 236 KB  
Article
Third-Order Noncanonical Neutral Delay Differential Equations: Nonexistence of Kneser Solutions via Myshkis Type Criteria
by Gunasekaran Nithyakala, George E. Chatzarakis, Govindasamy Ayyappan and Ethiraju Thandapani
Mathematics 2024, 12(18), 2847; https://doi.org/10.3390/math12182847 - 13 Sep 2024
Cited by 3 | Viewed by 857
Abstract
The purpose of this paper is to add some new asymptotic and oscillatory results for third-order neutral delay differential equations with noncanonical operators. Without assuming any extra conditions, by using the canonical transform technique, the studied equation is changed to a canonical type [...] Read more.
The purpose of this paper is to add some new asymptotic and oscillatory results for third-order neutral delay differential equations with noncanonical operators. Without assuming any extra conditions, by using the canonical transform technique, the studied equation is changed to a canonical type equation, and this reduces the number of classes of nonoscillatory solutions into two instead of four. Then, we obtain Myshkis type sufficient conditions for the nonexistence of Kneser type solutions for the studied equation. Finally, employing these newly obtained criteria, we provide conditions for the oscillation of all solutions of the studied equation. Examples are presented to illustrate the importance and the significance of the main results. Full article
18 pages, 333 KB  
Article
Kneser-Type Oscillation Criteria for Half-Linear Delay Differential Equations of Third Order
by Fahd Masood, Clemente Cesarano, Osama Moaaz, Sameh S. Askar, Ahmad M. Alshamrani and Hamdy El-Metwally
Symmetry 2023, 15(11), 1994; https://doi.org/10.3390/sym15111994 - 29 Oct 2023
Cited by 10 | Viewed by 1424
Abstract
This paper delves into the analysis of oscillation characteristics within third-order quasilinear delay equations, focusing on the canonical case. Novel sufficient conditions are introduced, aimed at discerning the nature of solutions—whether they exhibit oscillatory behavior or converge to zero. By expanding the literature, [...] Read more.
This paper delves into the analysis of oscillation characteristics within third-order quasilinear delay equations, focusing on the canonical case. Novel sufficient conditions are introduced, aimed at discerning the nature of solutions—whether they exhibit oscillatory behavior or converge to zero. By expanding the literature, this study enriches the existing knowledge landscape within this field. One of the foundations on which we rely in proving the results is the symmetry between the positive and negative solutions, so that we can, using this feature, obtain criteria that guarantee the oscillation of all solutions. The paper enhances comprehension through the provision of illustrative examples that effectively showcase the outcomes and implications of the established findings. Full article
11 pages, 283 KB  
Article
Investigation of the Oscillatory Properties of Solutions of Differential Equations Using Kneser-Type Criteria
by Yousef Alnafisah and Osama Moaaz
Axioms 2023, 12(9), 876; https://doi.org/10.3390/axioms12090876 - 13 Sep 2023
Viewed by 1351
Abstract
This study investigates the oscillatory properties of a fourth-order delay functional differential equation. This study’s methodology is built around two key tenets. First, we propose optimized relationships between the solution and its derivatives by making use of some improved monotonic features. By using [...] Read more.
This study investigates the oscillatory properties of a fourth-order delay functional differential equation. This study’s methodology is built around two key tenets. First, we propose optimized relationships between the solution and its derivatives by making use of some improved monotonic features. By using a comparison technique to connect the oscillation of the studied equation with some second-order equations, the second aspect takes advantage of the significant progress made in the study of the oscillation of second-order equations. Numerous applications of functional differential equations of the neutral type served as the inspiration for the study of a subclass of these equations. Full article
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