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

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Publikace nespadá pod Filozofickou fakultu, ale pod Přírodovědeckou fakultu. Oficiální stránka publikace je na webu muni.cz.
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ŠIŠOLÁKOVÁ Jiřina

Rok publikování 2024
Druh Článek v odborném periodiku
Časopis / Zdroj Open Mathematics
Fakulta / Pracoviště MU

Přírodovědecká fakulta

Citace
www https://www.degruyter.com/document/doi/10.1515/math-2024-0012/html
Doi http://dx.doi.org/10.1515/math-2024-0012
Klíčová slova linear equation; oscillation theory; non-oscillation; Riccati equation; Pr & uuml;fer angle
Popis 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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