Opuscula Math. 45, no. 6 (2025), 785-806
https://doi.org/10.7494/OpMath.2025.45.6.785

 
Opuscula Mathematica

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

Petr Hasil
Jiřina Šišoláková
Michal Veselý

Abstract. 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.

Keywords: comparison theorem, oscillation theory, non-oscillation, half-linear equation, Riccati equation, Prüfer angle.

Mathematics Subject Classification: 34C10, 34C15.

Full text (pdf)

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  • Jiřina Šišoláková
  • ORCID iD https://orcid.org/0000-0002-7487-5606
  • Masaryk University, Faculty of Science, Department of Mathematics and Statistics, Kotlářská 2, CZ-611 37 Brno, Czech Republic
  • Michal Veselý (corresponding author)
  • ORCID iD https://orcid.org/0000-0001-5306-7127
  • Masaryk University, Faculty of Science, Department of Mathematics and Statistics, Kotlářská 2, CZ-611 37 Brno, Czech Republic
  • Communicated by Marek Galewski.
  • Received: 2025-03-20.
  • Revised: 2025-10-18.
  • Accepted: 2025-10-22.
  • Published online: 2025-12-08.
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Cite this article as:
Petr Hasil, Jiřina Šišoláková, Michal Veselý, Comparison theorems for oscillation and non-oscillation of perturbed Euler type equations, Opuscula Math. 45, no. 6 (2025), 785-806, https://doi.org/10.7494/OpMath.2025.45.6.785

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