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Nonrectifiable oscillatory solutions of second order linear differential equations

Takanao Kanemitsu; Satoshi Tanaka — 2017

Archivum Mathematicum

The second order linear differential equation ${(p (x) y^{'})}^{'} + q (x) y = 0, x \in (0, x_{0}]$ is considered, where $p$ , $q \in C^{1} (0, x_{0}]$ , $p (x) > 0$ , $q (x) > 0$ for $x \in (0, x_{0}]$ . Sufficient conditions are established for every nontrivial solutions to be nonrectifiable oscillatory near $x = 0$ without the Hartman–Wintner condition.

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