系数含有自然对数幂次的线性方程的振动判据

Monatshefte für Mathematik Pub Date : 2023-10-13 DOI:10.1007/s00605-023-01910-6

Petr Hasil, Michal Pospíšil, Jiřina Šišoláková, Michal Veselý

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摘要

摘要应用自适应普勒费尔角的平均技术，得到了系数由自然对数幂与一般(有界或无界)连续函数积构成的线性二阶微分方程的振动判据。给出的判据用新的推论和实例加以说明。这种新颖性是由于在无界区间上使用了平均技术。

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Oscillation criterion for linear equations with coefficients containing powers of natural logarithm

Abstract Applying an averaging technique for the adapted Prüfer angle, we obtain an oscillation criterion for linear second order differential equations whose coefficients consist of products of powers of natural logarithm and general (bounded or unbounded) continuous functions. The presented criterion is illustrated by new corollaries and examples. The novelty is caused by the used averaging technique over unbounded intervals.

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Monatshefte für Mathematik

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