Amended Criteria for Testing the Asymptotic and Oscillatory Behavior of Solutions of Higher-Order Functional Differential Equations

Almarri, Barakah; Masood, Fahd; Moaaz, Osama; Muhib, Ali

doi:10.3390/axioms11120718

Cited by 6 publications

(6 citation statements)

References 23 publications

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“…Proof. Similar to the argument presented in the proof of Lemma 9, we obtain the Equation (17). Considering (Y 7,1,m ), we deduce that…”

Section: Category ωsupporting

confidence: 59%

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New Monotonic Properties for Solutions of a Class of Functional Differential Equations and Their Applications

Masood,

Moaaz,

AlNemer

et al. 2023

Symmetry

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This paper delves into the enhancement of asymptotic and oscillatory behaviors in solutions to even-order neutral differential equations with multiple delays. The main objective is to establish improved inequalities to advance the understanding of oscillation theory for these equations. The paper’s approach is centered on improving the understanding of the intricate relationship between solutions and their corresponding functions. This is achieved by harnessing the modified monotonic properties of positive solutions, which provide valuable insights into oscillation behavior. Furthermore, leveraging the symmetry between positive and negative solutions, we derived criteria that ensure oscillation for all solutions, with a specific emphasis on excluding only positive solutions. To illustrate the significance of our findings, we provide an illustrative example.

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“…Proof. Similar to the argument presented in the proof of Lemma 9, we obtain the Equation (17). Considering (Y 7,1,m ), we deduce that…”

Section: Category ωsupporting

confidence: 59%

“…[12][13][14][15], have directed their efforts toward understanding neutral DEs. Furthermore, Moaaz et al extended this analytical exploration to encompass even-order equations in their publications, such as [16,17].…”

Section: Introductionmentioning

confidence: 99%

New Monotonic Properties for Solutions of a Class of Functional Differential Equations and Their Applications

Masood,

Moaaz,

AlNemer

et al. 2023

Symmetry

Self Cite

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“…We deduce directly from (20) and from property L 1 U that < 1 is increasing. Using this in (18), additionally, taking into account (13), we obtain…”

Section: Nonexistence Of N 2 -Type Solutionsmentioning

confidence: 99%

“…While even-order delay differential equations have received more attention than oddorder ones, the study of DDEs in general has gained traction in recent years. Interested readers can refer to various studies, including Parhi and Das [3], Parhi and Padhi [4,5], Baculikova et al [6], Dzurina [7], Bohner et al [8], Chatzarakis et al [9,10], Moaaz [11], and Almarri et al [12,13] and the references mentioned therein.…”

Section: Introductionmentioning

confidence: 99%

Kneser-Type Oscillation Criteria for Half-Linear Delay Differential Equations of Third Order

Masood,

Cesarano,

Moaaz

et al. 2023

Symmetry

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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.

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“…In the non-canonical case, several studies have concentrated on analyzing the oscillation criteria for even-order neutral delay differential equations. These studies include the works of Moaaz et al [17], Almari et al [18], another study by Bohner et al [19], and Jadlovska [20]. The investigations conducted have provided valuable insights regarding the oscillatory behavior and dynamics exhibited by these equations.…”

Section: Introductionmentioning

confidence: 99%

New Conditions for Testing the Asymptotic Behavior of Solutions of Odd-Order Neutral Differential Equations with Multiple Delays

Masood

Moaaz

Askar

et al. 2023

Axioms

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The purpose of this research is to investigate the asymptotic and oscillatory characteristics of odd-order neutral differential equation solutions with multiple delays. The relationship between the solution and its derivatives of different orders, as well as their related functions, must be understood in order to determine the oscillation terms of the studied equation. In order to contribute to this subject, we create new and significant relationships and inequalities. We use these relationships to create conditions in which positive and N-Kneser solutions of the considered equation are excluded. To obtain these terms, we employ the comparison method and the Riccati technique. Furthermore, we use the relationships obtained to create new criteria, so expanding the existing literature on the field. Finally, we provide an example from the general case to demonstrate the results’ significance. The findings given in this work provide light on the behavior of odd-order neutral differential equation solutions with multiple delays.

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Amended Criteria for Testing the Asymptotic and Oscillatory Behavior of Solutions of Higher-Order Functional Differential Equations

Cited by 6 publications

References 23 publications

New Monotonic Properties for Solutions of a Class of Functional Differential Equations and Their Applications

New Monotonic Properties for Solutions of a Class of Functional Differential Equations and Their Applications

Kneser-Type Oscillation Criteria for Half-Linear Delay Differential Equations of Third Order

New Conditions for Testing the Asymptotic Behavior of Solutions of Odd-Order Neutral Differential Equations with Multiple Delays

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