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Comparison theorems for oscillation and non-oscillation of perturbed Euler type equations

Hasil Petr, Šišoláková Jiřina, Veselý Michal

Opuscula Mathematica

2025

Vol. 45, no. 6

785--806

The aim of this paper is to present two comparison theorems. These results enable to describe the oscillation behavior of second order Euler type half-linear differential equations with perturbations in both terms using previously obtained oscillation and non-oscillation criteria. We point out that the comparison theorems are easy to use. This fact is also illustrated by a simple example. In addition, the number of perturbations is arbitrary and the last perturbations can be given by very general continuous functions. Note that the presented results are new even in the case of linear equations.