Theoretical analysis establishes sharper oscillation criteria for second-order neutral dynamic equations on time scales, suggesting improved predictive accuracy for nonlinear systems.
This paper establishes new sufficient conditions for the oscillation of a class of second-order nonlinear neutral dynamic equations on time scales. To obtain criteria that are both simple and easily verifiable, the original nonlinear equation is first converted into an appropriate linearised form. By employing improved monotonic properties of nonoscillatory solutions, sharper oscillation results are derived, which extend and refine several existing criteria in the literature. The effectiveness and applicability of the proposed conditions are demonstrated through three carefully constructed examples, and the results are validated using MATLAB simulations.
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Grace et al. (2026) studied this question.
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