Publication details

Non-oscillation of linear differential equations with coefficients containing powers of natural logarithm

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Authors

ŠIŠOLÁKOVÁ Jiřina

Year of publication 2024
Type Article in Periodical
Magazine / Source Open Mathematics
MU Faculty or unit

Faculty of Science

Citation
Web https://www.degruyter.com/document/doi/10.1515/math-2024-0012/html
Doi http://dx.doi.org/10.1515/math-2024-0012
Keywords linear equation; oscillation theory; non-oscillation; Riccati equation; Pr & uuml;fer angle
Description We study linear differential equations whose coefficients consist of products of powers of natural logarithm and general continuous functions. We derive conditions that guarantee the non-oscillation of all non-trivial solutions of the treated type of equations. The conditions are formulated as a non-oscillation criterion, which is the counterpart of a previously obtained oscillation theorem. Therefore, from the presented main result, it follows that the analysed equations are conditionally oscillatory. The used method is based on averaging techniques for the combination of the generalized adapted Pr & uuml;fer angle and the modified Riccati transformation. This article is finished by new corollaries and examples.
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