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

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.