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

• Autorzy: Hasil Petr , Šišoláková Jiřina , Veselý Michal

Identyfikatory

DOI

10.7494/OpMath.2025.45.6.785

• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

comparison theorem; oscillation theory; non-oscillation; half-linear equation; Riccati equation; Prufer angle

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2025
• Tom: Vol. 45, no. 6
• Strony: 785--806
• Opis fizyczny: Bibliogr. 62 poz.

Twórcy

autor

Hasil Petr

• Masaryk University, Faculty of Science, Department of Mathematics and Statistics, Kotlářská 2, CZ-611 37 Brno, Czech Republic

• https://orcid.org/0000-0002-8039-688X

autor

Šišoláková Jiřina

• Masaryk University, Faculty of Science, Department of Mathematics and Statistics, Kotlářská 2, CZ-611 37 Brno, Czech Republic

• https://orcid.org/0000-0002-7487-5606

autor

Veselý Michal

• Masaryk University, Faculty of Science, Department of Mathematics and Statistics, Kotlářská 2, CZ-611 37 Brno, Czech Republic

• https://orcid.org/0000-0001-5306-7127

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Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr POPUL/SP/0154/2024/02 w ramach programu "Społeczna odpowiedzialność nauki II" - moduł: Popularyzacja nauki (2025)