Oscillation criteria for mixed neutral differential equations

Alsharidi, Abdulaziz khalid; Muhib, Ali

doi:10.3934/math.2024703

MATH

2024

DOI: 10.3934/math.2024703

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Oscillation criteria for mixed neutral differential equations

Abdulaziz khalid Alsharidi,

Ali Muhib

Abstract: <abstract><p>In this study, we aim to contribute to the increasing interest in functional differential equations by obtaining new theorems for the oscillation of second-order neutral differential equations of mixed type in a non-canonical form. The results obtained here improve and extend those reported in the literature. The applicability of the results is illustrated by several examples.</p></abstract>

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Cited by 3 publications

References 40 publications

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Forced-Perturbed Fractional Differential Equations of Higher Order: Asymptotic Properties of Non-Oscillatory Solutions

Grace,

Chhatria,

Kaleeswari

et al. 2024

Fractal Fract

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This study investigates the asymptotic behavior of non-oscillatory solutions to forced-perturbed fractional differential equations with the Caputo fractional derivative. The main aim is to unify the Beta Integral Lemma (Lemma 2) and the Gamma Integral Lemma (Lemma 3) into a single framework. By combining these two powerful tools, we propose new criteria that effectively characterize the asymptotic behavior of non-oscillatory solutions to the given equations. The analysis of such solutions has significant implications in the fields of oscillation and stability theory. Notably, our findings extend prior work by exploring a wider range of equations with more general functions and coefficients, thereby broadening the applicability and deepening the understanding of both asymptotic and oscillatory behaviors. Moreover, the criteria we introduce offer improvements over previous approaches, as demonstrated by the example provided, which highlights the advantages of our results in comparison to earlier methods.

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Forced-Perturbed Fractional Differential Equations of Higher Order: Asymptotic Properties of Non-Oscillatory Solutions

Grace,

Chhatria,

Kaleeswari

et al. 2024

Fractal Fract

View full text Add to dashboard Cite

show abstract

Nonlinear Neutral Delay Differential Equations: Novel Criteria for Oscillation and Asymptotic Behavior

Batiha,

Alshammari,

Aldosari

et al. 2025

Mathematics

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This research deals with the study of the oscillatory behavior of solutions of second-order differential equations containing neutral conditions, both in sublinear and superlinear terms, with a focus on the noncanonical case. The research provides a careful analysis of the monotonic properties of solutions and their derivatives, paving the way for a deeper understanding of this complex behavior. The research is particularly significant as it extends the scope of previous studies by addressing more complex forms of neutral differential equations. Using the linearization technique, strict conditions are developed that exclude the existence of positive solutions, which allows the formulation of innovative criteria for determining the oscillatory behavior of the studied equations. This research highlights the theoretical and applied aspects of this mathematical phenomenon, which contributes to enhancing the scientific understanding of differential equations with neutral conditions. To demonstrate the effectiveness of the results, the research includes two illustrative examples that prove the validity and importance of the proposed methodology. This work represents a qualitative addition to the mathematical literature, as it lays new foundations and opens horizons for future studies in this vital field.

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Neutral Emden–Fowler Differential Equation of Second Order: Oscillation Criteria of Coles Type

Nabih,

Al-Jaser,

Moaaz

2024

Symmetry

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In this work, we study the asymptotic and oscillatory behavior of solutions to the second-order general neutral Emden–Fowler differential equation (avηxvz′v)′ + qvFxgv = 0, where v≥v0 and the corresponding function z = x + px∘h. Besides the importance of equations of the neutral type, studying the qualitative behavior of solutions to these equations is rich in analytical points and interesting issues. We begin by finding the monotonic features of positive solutions. The new properties contribute to obtaining new and improved relationships between x and z for use in studying oscillatory behavior. We present new conditions that exclude the existence of positive solutions to the examined equation, and then we establish oscillation criteria through the symmetry property between non-oscillatory solutions. We use the generalized Riccati substitution method, which enables us to apply the results to a larger area than the special cases of the considered equation. The new results essentially improve and extend previous results in the literature. We support this claim by applying the results to an example and comparing them with previous findings. Moreover, the reduction of our results to Euler’s differential equation introduces the well-known sharp oscillation criterion.

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Oscillation criteria for mixed neutral differential equations

Cited by 3 publications

References 40 publications

Forced-Perturbed Fractional Differential Equations of Higher Order: Asymptotic Properties of Non-Oscillatory Solutions

Forced-Perturbed Fractional Differential Equations of Higher Order: Asymptotic Properties of Non-Oscillatory Solutions

Nonlinear Neutral Delay Differential Equations: Novel Criteria for Oscillation and Asymptotic Behavior

Neutral Emden–Fowler Differential Equation of Second Order: Oscillation Criteria of Coles Type

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