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

Masood, Fahd; Cesarano, Clemente; Moaaz, Osama; Askar, Sameh S.; Alshamrani, Ahmad M.; El-Metwally, Hamdy

doi:10.3390/sym15111994

Cited by 5 publications

(1 citation statement)

References 20 publications

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“…They discussed the criteria ensuring that all solutions oscillate or tend to zero. Subsequently, Masood et al [44] extended this study to encompass the third-order quasilinear delay differential equation…”

Section: Introductionmentioning

confidence: 99%

Asymptotic and Oscillatory Properties of Third-Order Differential Equations with Multiple Delays in the Noncanonical Case

Alrashdi,

Moaaz,

Alqawasmi

et al. 2024

Mathematics

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This paper investigates the asymptotic and oscillatory properties of a distinctive class of third-order linear differential equations characterized by multiple delays in a noncanonical case. Employing the comparative method and the Riccati method, we introduce the novel and rigorous criteria to discern whether the solutions of the examined equation exhibit oscillatory behavior or tend toward zero. Our study contributes to the existing literature by presenting theories that extend and refine the understanding of these properties in the specified context. To validate our findings and demonstrate their applicability in a general setting, we offer two illustrative examples, affirming the robustness and validity of our proposed criteria.

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Section: Introductionmentioning

confidence: 99%

Asymptotic and Oscillatory Properties of Third-Order Differential Equations with Multiple Delays in the Noncanonical Case

Alrashdi,

Moaaz,

Alqawasmi

et al. 2024

Mathematics

Self Cite

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Third-Order Neutral Differential Equations with Non-Canonical Forms: Novel Oscillation Theorems

Almarri,

Batiha,

Bazighifan

et al. 2024

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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.

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Third-Order Nonlinear Semi-Canonical Functional Differential Equations: Oscillation via New Canonical Transform

Chandrasekaran,

Chatzarakis,

Sakthivel

et al. 2024

Mathematics

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This paper focuses on the oscillatory properties of the third-order semi-canonical nonlinear delay differential equation. By using the new canonical transform method, we transformed the studied equation into a canonical-type equation, which simplified the examination of the studied equation. The obtained oscillation results are new and complement the existing results mentioned in the literature. Examples are provided to illustrate the importance and novelty of the main results.

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

Cited by 5 publications

References 20 publications

Asymptotic and Oscillatory Properties of Third-Order Differential Equations with Multiple Delays in the Noncanonical Case

Asymptotic and Oscillatory Properties of Third-Order Differential Equations with Multiple Delays in the Noncanonical Case

Third-Order Neutral Differential Equations with Non-Canonical Forms: Novel Oscillation Theorems

Third-Order Nonlinear Semi-Canonical Functional Differential Equations: Oscillation via New Canonical Transform

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