Turkish Journal of Mathematics
Abstract
In this paper, we examine the oscillatory behavior of the first-order linear delay difference equation Δy(n) + p(n) y(τ(n)) = 0, n ∈ ℕ0. It is known in the literature that, for any C > 0, the condition lim supn→∞ ∑i=τ(n)n p(i) > C, with τ(n) nonmonotone, is not, in general, sufficient to establish the oscillation of the difference equation. We prove that, for certain classes of difference equations, the aforementioned condition is sufficient to ensure the oscillation property. Specific oscillation results are presented in terms of the limit superior. We obtain several novel results by employing new methods and techniques to analyze the properties of positive solutions of the equation under study. Two illustrative examples are included to demonstrate the effectiveness of our results.
DOI
10.55730/1300-0098.3662
Keywords
Oscillation, delay difference equations, nonmonotone delays
First Page
458
Last Page
474
Publisher
The Scientific and Technological Research Council of Türkiye (TÜBİTAK)
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
Recommended Citation
ATTIA, E, & CHATZARAKIS, G (2026). Oscillation properties of first-order difference equations with nonmonotone delays: new insights and criteria. Turkish Journal of Mathematics 50 (3): 458-474. https://doi.org/10.55730/1300-0098.3662
