Introduces new criteria for oscillation in nonlinear dynamic equations, suggesting broader applicability.
In this paper the authors introduce novel criteria for the oscillation of nonlinear higher-order dynamic equations with deviating arguments. The primary goal is to linearize the equation in such a way that the oscillatory behavior of solutions can be inferred from the oscillation of its linear counterpart. Additionally, the study presents new oscillation criteria by comparing the nonlinear equation to well-understood n th-order linear equations. The results obtained are original, and they enhance and connect various existing oscillation criteria found in the literature. Examples are provided to demonstrate the findings.
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Graef et al. (2026) studied this question.
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