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Mathematics
Volume 14
Issue 3
10.3390/math14030446
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This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

Oscillation Results for Difference Equations with Several Non-Monotone Advanced Arguments

by
Md Taufiq Nasseef
1,*,
George Chatzarakis
2 and
Emad Attia
1
1
Department of Mathematics, College of Sciences and Humanities, Prince Sattam Bin Abdulaziz University, Alkharj 11942, Saudi Arabia
2
Department of Electrical and Electronic Engineering Educators, School of Pedagogical and Technological Education (ASPETE) Athens, 15122 Marousi, Greece
*
Author to whom correspondence should be addressed.
Mathematics 2026, 14(3), 446; https://doi.org/10.3390/math14030446
Submission received: 18 December 2025 / Revised: 23 January 2026 / Accepted: 24 January 2026 / Published: 27 January 2026
(This article belongs to the Section C1: Difference and Differential Equations)
Versions Notes

Abstract

We investigate the oscillatory behavior of a first-order linear difference equation with several advanced arguments. New sufficient conditions for oscillation are established, and we show, through carefully constructed counterexamples, that many well-known oscillation criteria for equations with a single advanced argument fail to generalize to the several-argument setting, even when each advanced argument is increasing. Several illustrative examples are also provided to demonstrate the sharpness and practical effectiveness of the obtained conditions and to highlight their clear improvements over all existing results in the literature.
Keywords: difference and differential equations; oscillation; several non-monotone advanced arguments difference and differential equations; oscillation; several non-monotone advanced arguments

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MDPI and ACS Style

Nasseef, M.T.; Chatzarakis, G.; Attia, E. Oscillation Results for Difference Equations with Several Non-Monotone Advanced Arguments. Mathematics 2026, 14, 446. https://doi.org/10.3390/math14030446

AMA Style

Nasseef MT, Chatzarakis G, Attia E. Oscillation Results for Difference Equations with Several Non-Monotone Advanced Arguments. Mathematics. 2026; 14(3):446. https://doi.org/10.3390/math14030446

Chicago/Turabian Style

Nasseef, Md Taufiq, George Chatzarakis, and Emad Attia. 2026. "Oscillation Results for Difference Equations with Several Non-Monotone Advanced Arguments" Mathematics 14, no. 3: 446. https://doi.org/10.3390/math14030446

APA Style

Nasseef, M. T., Chatzarakis, G., & Attia, E. (2026). Oscillation Results for Difference Equations with Several Non-Monotone Advanced Arguments. Mathematics, 14(3), 446. https://doi.org/10.3390/math14030446

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