Second-order noncanonical difference equations with a sublinear neutral term: improved oscillation criteria
DOI:
https://doi.org/10.24193/subbmath.2026.3.6Keywords:
Oscillation, non-oscillation, neutral difference equation, sublinear, noncanonical formAbstract
The topic under consideration is the study of the oscillatory behaviour of the second-order nonlinear neutral difference equation of the form \[ \Delta[r(\nu)(\Delta (\mathcal{V}(\nu)-q(\nu)\mathcal{V}^{\gamma}(\delta(\nu))))^{\alpha}] +\mathcal{P}(\nu)\mathcal{V}^{\beta}(\eta(\nu))=0,\;\nu\geq \nu_{0} \] of noncanonical type. We give an answer to a question raised in Remark 4.1 of [Mediterr. J. Math. 18, 253 (2021)]. Our findings basically improve or generalise the work of Dinakar et al. [Int. J. Appl. Comput. Math. 5 164 (2019)], Seghar et al. [Tamkang J. Math. 46, 441-451 (2015)] and Thandapani et al. [Dyn. Contin. Discrete Impuls. Syst. Ser. A. Math. Anal. 19, 543–469 (2012)]. Two examples are given to demonstrate the analytical results. Finally, we define two open problems for future research.
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