@Article{Džurina2026,
author = "Džurina, Jozef and Baculíková, Blanka",
title = "Comparison theorems for property (B) of the third-order differential equations with deviating arguments",
journal = "Opuscula Math.",
year = "2026",
volume = "46",
number = "3",
pages = "291--304",
doi = "https://doi.org/10.7494/OpMath.202605181",
url = "https://doi.org/10.7494/OpMath.202605181",
abstract = "The aim of this paper is to introduce a new comparison theorem (in both delayed and advanced cases) that allows us to investigate the properties of third-order differential equations with quasi-derivatives \[(r_1(t)(r_2(t)y'(t))')'-p(t)y(\tau(t))=0\] using the following simpler differential equations \[(r(t)(r(t)z'(t))')'-p(t)z(\tau(t))=0\] and \[y'''(t)-q(t)y(\sigma(t))=0.\] The obtained comparison principles allow for the immediate transcription of the oscillatory results known for the simpler equations into studied equation with quasi-derivatives. The progress achieved will be illustrated through several examples.",
keywords = "canonical equation, comparison theorem, property (B)",
issn = "1232-9274"
}