Oscillatory Behavior of Semi-canonical Nonlinear Neutral Differential Equations of Third-Order Via Comparison Principles

Thandapani, E.; Göktürk, Batuhan; Özdemir, Orhan; Tunç, Ercan

doi:10.1007/s12346-022-00731-6

Cited by 2 publications

(1 citation statement)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Furthermore, Refs. [16][17][18][19][20][21] show how investigations of odd-order equations have evolved. Moreover, one may trace the variation of fractional DDEs in Survey [22].…”

Section: Introductionmentioning

confidence: 99%

Kamenev-Type Criteria for Testing the Asymptotic Behavior of Solutions of Third-Order Quasi-Linear Neutral Differential Equations

Alrashdi,

Albalawi,

Muhib

et al. 2024

Mathematics

View full text Add to dashboard Cite

This paper aims to study the asymptotic properties of nonoscillatory solutions (eventually positive or negative) of a class of third-order canonical neutral differential equations. We use Riccati substitution to reduce the order of the considered equation, and then we use the Philos function class to obtain new criteria of the Kamenev type, which guarantees that all nonoscillatory solutions converge to zero. This approach is characterized by the possibility of applying its conditions to a wider area of equations. This is not the only aspect that distinguishes our results; we also use improved relationships between the solution and the corresponding function, which in turn is reflected in a direct improvement of the criteria. The findings in this article extend and generalize previous findings in the literature and also improve some of these findings.

show abstract

“…Furthermore, Refs. [16][17][18][19][20][21] show how investigations of odd-order equations have evolved. Moreover, one may trace the variation of fractional DDEs in Survey [22].…”

Section: Introductionmentioning

confidence: 99%

Kamenev-Type Criteria for Testing the Asymptotic Behavior of Solutions of Third-Order Quasi-Linear Neutral Differential Equations

Alrashdi,

Albalawi,

Muhib

et al. 2024

Mathematics

View full text Add to dashboard Cite

show abstract

An Improved Relationship between the Solution and Its Corresponding Function in Fourth-Order Neutral Differential Equations and Its Applications

2023

View full text Add to dashboard Cite

This work aims to derive new inequalities that improve the asymptotic and oscillatory properties of solutions to fourth-order neutral differential equations. The relationships between the solution and its corresponding function play an important role in the oscillation theory of neutral differential equations. Therefore, we improve these relationships based on the modified monotonic properties of positive solutions. Additionally, we set new conditions that confirm the absence of positive solutions and thus confirm the oscillation of all solutions of the considered equation. We finally explain the importance of the new inequalities by applying our results to some special cases of the studied equation, as well as comparing them with previous results in the literature.

show abstract

Oscillatory Behavior of Semi-canonical Nonlinear Neutral Differential Equations of Third-Order Via Comparison Principles

Cited by 2 publications

References 23 publications

Kamenev-Type Criteria for Testing the Asymptotic Behavior of Solutions of Third-Order Quasi-Linear Neutral Differential Equations

Kamenev-Type Criteria for Testing the Asymptotic Behavior of Solutions of Third-Order Quasi-Linear Neutral Differential Equations

An Improved Relationship between the Solution and Its Corresponding Function in Fourth-Order Neutral Differential Equations and Its Applications

Contact Info

Product

Resources

About