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Search Results (8)

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Keywords = fourth-order p-Laplacian differential equations

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10 pages, 260 KiB  
Article
Differential Equations of Fourth-Order with p-Laplacian-like Operator: Oscillation Theorems
by Omar Bazighifan, Nawa Alshammari, Khalil S. Al-Ghafri and Loredana Florentina Iambor
Mathematics 2024, 12(22), 3558; https://doi.org/10.3390/math12223558 - 14 Nov 2024
Cited by 1 | Viewed by 954
Abstract
In this work, we find new oscillation criteria for fourth-order advanced differential equations with a p-Laplace-type operator. We established our results through a comparison method with integral averaging and Riccati techniques to obtain new oscillatory properties for the considered equation. Our criteria substantially [...] Read more.
In this work, we find new oscillation criteria for fourth-order advanced differential equations with a p-Laplace-type operator. We established our results through a comparison method with integral averaging and Riccati techniques to obtain new oscillatory properties for the considered equation. Our criteria substantially simplify and complement a number of existing ones. We give some examples to illustrate the significance of the obtained results. Full article
(This article belongs to the Special Issue Differential Equations with Boundary Value Problems: Theory and Applications)
23 pages, 353 KiB  
Article
Asymptotic and Oscillatory Analysis of Fourth-Order Nonlinear Differential Equations with p-Laplacian-like Operators and Neutral Delay Arguments
by Mansour Alatwi, Osama Moaaz, Wedad Albalawi, Fahd Masood and Hamdy El-Metwally
Mathematics 2024, 12(3), 470; https://doi.org/10.3390/math12030470 - 1 Feb 2024
Cited by 6 | Viewed by 1476
Abstract
This paper delves into the asymptotic and oscillatory behavior of all classes of solutions of fourth-order nonlinear neutral delay differential equations in the noncanonical form with damping terms. This research aims to improve the relationships between the solutions of these equations and their [...] Read more.
This paper delves into the asymptotic and oscillatory behavior of all classes of solutions of fourth-order nonlinear neutral delay differential equations in the noncanonical form with damping terms. This research aims to improve the relationships between the solutions of these equations and their corresponding functions and derivatives. By refining these relationships, we unveil new insights into the asymptotic properties governing these solutions. These insights lead to the establishment of improved conditions that ensure the nonexistence of any positive solutions to the studied equation, thus obtaining improved oscillation criteria. In light of the broader context, our findings extend and build upon the existing literature in the field of neutral differential equations. To emphasize the importance of the results and their applicability, this paper concludes with some examples. Full article
(This article belongs to the Special Issue The Theory of Differential Equations and Their Applications)
11 pages, 289 KiB  
Article
Oscillatory Properties of Fourth-Order Advanced Differential Equations
by Alanoud Almutairi, Ali Hasan Ali, Omar Bazighifan and Loredana Florentina Iambor
Mathematics 2023, 11(6), 1391; https://doi.org/10.3390/math11061391 - 13 Mar 2023
Cited by 6 | Viewed by 1660
Abstract
This paper presents a study on the oscillatory behavior of solutions to fourth-order advanced differential equations involving p-Laplacian-like operator. We obtain oscillation criteria using techniques from first and second-order delay differential equations. The results of this work contribute to a deeper understanding [...] Read more.
This paper presents a study on the oscillatory behavior of solutions to fourth-order advanced differential equations involving p-Laplacian-like operator. We obtain oscillation criteria using techniques from first and second-order delay differential equations. The results of this work contribute to a deeper understanding of fourth-order differential equations and their connections to various branches of mathematics and practical sciences. The findings emphasize the importance of continued research in this area. Full article
(This article belongs to the Special Issue Qualitative Analysis of Differential Equations: Theory and Applications)
8 pages, 303 KiB  
Article
Symmetric and Non-Oscillatory Characteristics of the Neutral Differential Equations Solutions Related to p-Laplacian Operators
by Barakah Almarri, Ali Hasan Ali, Khalil S. Al-Ghafri, Alanoud Almutairi, Omar Bazighifan and Jan Awrejcewicz
Symmetry 2022, 14(3), 566; https://doi.org/10.3390/sym14030566 - 13 Mar 2022
Cited by 28 | Viewed by 2431
Abstract
The main purpose of this research was to use the comparison approach with a first-order equation to derive criteria for non-oscillatory solutions of fourth-order nonlinear neutral differential equations with p Laplacian operators. We obtained new results for the behavior of solutions to these [...] Read more.
The main purpose of this research was to use the comparison approach with a first-order equation to derive criteria for non-oscillatory solutions of fourth-order nonlinear neutral differential equations with p Laplacian operators. We obtained new results for the behavior of solutions to these equations, and we showed their symmetric and non-oscillatory characteristics. These results complement some previously published articles. To find out the effectiveness of these results and validate the proposed work, two examples were discussed at the end of the paper. Full article
(This article belongs to the Special Issue Symmetries of Difference Equations, Special Functions and Orthogonal Polynomials)
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10 pages, 286 KiB  
Article
New Criteria for Oscillation of Half-Linear Differential Equations with p-Laplacian-like Operators
by Omar Bazighifan, F. Ghanim, Jan Awrejcewicz, Khalil S. Al-Ghafri and Maryam Al-Kandari
Mathematics 2021, 9(20), 2584; https://doi.org/10.3390/math9202584 - 14 Oct 2021
Cited by 4 | Viewed by 1539
Abstract
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 [...] Read more.
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. Full article
10 pages, 756 KiB  
Article
Nonlinear Neutral Delay Differential Equations of Fourth-Order: Oscillation of Solutions
by Ravi P. Agarwal, Omar Bazighifan and Maria Alessandra Ragusa
Entropy 2021, 23(2), 129; https://doi.org/10.3390/e23020129 - 20 Jan 2021
Cited by 83 | Viewed by 3753
Abstract
The objective of this paper is to study oscillation of fourth-order neutral differential equation. By using Riccati substitution and comparison technique, new oscillation conditions are obtained which insure that all solutions of the studied equation are oscillatory. Our results complement some known results [...] Read more.
The objective of this paper is to study oscillation of fourth-order neutral differential equation. By using Riccati substitution and comparison technique, new oscillation conditions are obtained which insure that all solutions of the studied equation are oscillatory. Our results complement some known results for neutral differential equations. An illustrative example is included. Full article
(This article belongs to the Special Issue Nonlinear Dynamics and Analysis)
11 pages, 772 KiB  
Article
Improved Approach for Studying Oscillatory Properties of Fourth-Order Advanced Differential Equations with p-Laplacian Like Operator
by Omar Bazighifan and Thabet Abdeljawad
Mathematics 2020, 8(5), 656; https://doi.org/10.3390/math8050656 - 26 Apr 2020
Cited by 37 | Viewed by 2215
Abstract
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Differential/Difference Equations: Mathematical Modeling, Oscillation and Applications)
10 pages, 252 KiB  
Article
Infinitely Many Homoclinic Solutions for Fourth Order p-Laplacian Differential Equations
by Stepan Tersian
Mathematics 2020, 8(4), 505; https://doi.org/10.3390/math8040505 - 2 Apr 2020
Cited by 1 | Viewed by 1879
Abstract
The existence of infinitely many homoclinic solutions for the fourth-order differential equation [...] Read more.
The existence of infinitely many homoclinic solutions for the fourth-order differential equation φ p u ″ t ″ + w φ p u ′ t ′ + V ( t ) φ p u t = a ( t ) f ( t , u ( t ) ) , t ∈ R is studied in the paper. Here φ p ( t ) = t p − 2 t , p ≥ 2 , w is a constant, V and a are positive functions, f satisfies some extended growth conditions. Homoclinic solutions u are such that u ( t ) → 0 , | t | → ∞ , u ≠ 0 , known in physical models as ground states or pulses. The variational approach is applied based on multiple critical point theorem due to Liu and Wang. Full article
(This article belongs to the Special Issue Recent Investigations of Differential and Fractional Equations and Inclusions)
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