Powered by OpenAIRE graph
Found an issue? Give us feedback
image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/ Mathematicsarrow_drop_down
image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/
Mathematics
Article . 2025 . Peer-reviewed
License: CC BY
Data sources: Crossref
image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/
Mathematics
Article . 2025
Data sources: DOAJ
versions View all 2 versions
addClaim

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

Authors: Belal Batiha; Nawa Alshammari; Faten Aldosari; Fahd Masood; Omar Bazighifan;

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

Abstract

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.

Keywords

sublinear type, second order, superlinear type, QA1-939, neutral differential equation, oscillation, non-oscillation, Mathematics

  • BIP!
    Impact byBIP!
    selected citations
    These citations are derived from selected sources.
    This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    9
    popularity
    This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
    Top 10%
    influence
    This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    Average
    impulse
    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
    Top 10%
Powered by OpenAIRE graph
Found an issue? Give us feedback
selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
9
Top 10%
Average
Top 10%
gold