Novel oscillation criteria for second-order noncanonical neutral differential equations with sublinear term

In this research, novel oscillation conditions are established for a category of second-order sublinear neutral differential equations of noncanonical form. A suitable substitution was used to transform the equation containing the damping term into an equation without this term, and then Riccati’s method was applied to derive conditions that exclude positive solutions satisfying the equation under consideration. Based on this, theorems containing new criteria were established to guarantee the oscillatory behavior of all solutions of the equation under investigation. These results represent an extension and improvement of previous literature, as we have introduced less restrictive criteria. Two practical examples are also presented to illustrate the significance of these results in practical applications. This study opens new avenues for research into oscillation criteria for neutral equations with noncanonical forms.