This research explores oscillatory behaviour in third-order noncanonical equations, suggesting new criteria for solutions.
The aim of this study is to investigate the oscillatory behaviour of a new class of third-order advanced differential equations in their noncanonical form. By employing newly refined transformations, the noncanonical equation is converted into its canonical form. This transformation reduces the number of possible nonoscillatory solution categories from four to two. The present study is based on a thorough and comprehensive review of existing literature and introduces new oscillation criteria by the comparison principle and other analytical techniques. These criteria provide sufficient conditions for the oscillation of solutions without imposing additional restrictive assumptions. The validity and significance of the obtained results are demonstrated through illustrative examples.
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Althemairi et al. (2025) studied this question.
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