Analysis reveals new criteria for oscillation and convergence in equations with nonlinear delayed terms, indicating further investigations are needed.
The paper investigates the oscillation, zero-convergence, and solutions of second-orderneutral delay difference equations containing three nonlinear delayed terms with differentgrowth rates. By using positivity and monotonicity conditions on an auxiliary functionalong with divergence-type conditions on the coefficient sequences of the neutral anddelayed terms, the paper establishes new criteria that guarantee oscillation or convergenceof all solutions. These novel findings extend and enhance several of the existing oscillationcriteria established by the literature. Suggestions for further investigation are includedwith illustrative examples.
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Masaniammal et al. (2025) studied this question.
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