TY  - JOUR
ID  - Džurina2026
LB  - Džurina2026
AU  - Džurina, Jozef
AU  - Baculíková, Blanka
TI  - Comparison theorems for property (B) of the third-order differential equations with deviating arguments
ST  - Comparison theorems for property (B) of the third-order differential equations with deviating arguments
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2026
VL  - 46
IS  - 3
SP  - 291
EP  - 304
DO  - https://doi.org/10.7494/OpMath.202605181
UR  - https://doi.org/10.7494/OpMath.202605181
AB  - 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.
KW  - canonical equation
KW  - comparison theorem
KW  - property (B)
SN  - 1232-9274
ER  -