Comparison techniques for detection of nonoscillation in half‐linear differential equations of the second order

Jaroslav Jaroš

Mathematische Nachrichten, 2025, vol. 298, issue 6, 2060-2071

Abstract: We present a new comparison method which improves the classical Hille–Wintner theorem and its generalization to a pair of half‐linear differential equations of the second order by incorporating a solution of the Riccati‐type equation associated with the majorant nonoscillatory differential equation into the comparison inequality. Our results are formulated in terms of the weighted primitives of the coefficient functions of compared half‐linear differential equations.

Date: 2025
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