TY  - JOUR
ID  - Hasil2025
LB  - Hasil2025
AU  - Hasil, Petr
AU  - Šišoláková, Jiřina
AU  - Veselý, Michal
TI  - Comparison theorems for oscillation and non-oscillation of perturbed Euler type equations
ST  - Comparison theorems for oscillation and non-oscillation of perturbed Euler type equations
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2025
VL  - 45
IS  - 6
SP  - 785
EP  - 806
DO  - https://doi.org/10.7494/OpMath.2025.45.6.785
UR  - https://doi.org/10.7494/OpMath.2025.45.6.785
AB  - 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.
KW  - comparison theorem
KW  - oscillation theory
KW  - non-oscillation
KW  - half-linear equation
KW  - Riccati equation
KW  - Prüfer angle
SN  - 1232-9274
ER  -