Non-oscillation of linear differential equations with coefficients containing powers of natural logarithm
| Autoři | |
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| Rok publikování | 2024 |
| Druh | Článek v odborném periodiku |
| Časopis / Zdroj | Open Mathematics |
| Fakulta / Pracoviště MU | |
| Citace | ŠIŠOLÁKOVÁ, Jiřina. Non-oscillation of linear differential equations with coefficients containing powers of natural logarithm. Open Mathematics. De Gruyter, 2024, roč. 22, č. 1, s. 1-13. ISSN 2391-5455. Dostupné z: https://dx.doi.org/10.1515/math-2024-0012. |
| 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; Prufer 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 Prufer angle and the modified Riccati transformation. This article is finished by new corollaries and examples. |
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