Conditionally oscillatory linear differential equations with coefficients containing powers of natural logarithm

Petr Hasil; Michal Veselý; Petr Hasil; Michal Veselý

doi:10.3934/math.2022596

AIMS Mathematics

2022, Volume 7, Issue 6: 10681-10699. doi: 10.3934/math.2022596

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Research article

Conditionally oscillatory linear differential equations with coefficients containing powers of natural logarithm

Petr Hasil ,
Michal Veselý ^,

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

Received: 08 January 2022 Revised: 04 March 2022 Accepted: 11 March 2022 Published: 30 March 2022
MSC : 34C10

In this paper, we study linear differential equations whose coefficients consist of products of powers of natural logarithm and very general continuous functions. Recently, using the Riccati transformation, we have identified a new type of conditionally oscillatory linear differential equations together with the critical oscillation constant. The studied equations are a generalization of these equations. Applying the modified Prüfer angle, we prove that they remain conditionally oscillatory with the same critical oscillation constant.
- linear equation,
- differential equation,
- conditional oscillation,
- non-oscillation,
- logarithm
Citation: Petr Hasil, Michal Veselý. Conditionally oscillatory linear differential equations with coefficients containing powers of natural logarithm[J]. AIMS Mathematics, 2022, 7(6): 10681-10699. doi: 10.3934/math.2022596

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Abstract

In this paper, we study linear differential equations whose coefficients consist of products of powers of natural logarithm and very general continuous functions. Recently, using the Riccati transformation, we have identified a new type of conditionally oscillatory linear differential equations together with the critical oscillation constant. The studied equations are a generalization of these equations. Applying the modified Prüfer angle, we prove that they remain conditionally oscillatory with the same critical oscillation constant.

References

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