# Nonrectifiable oscillatory solutions of second order linear differential equations

Archivum Mathematicum (2017)

• Volume: 053, Issue: 4, page 193-201
• ISSN: 0044-8753

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## Abstract

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The second order linear differential equation ${\left(p\left(x\right){y}^{\text{'}}\right)}^{\text{'}}+q\left(x\right)y=0\phantom{\rule{0.166667em}{0ex}},\phantom{\rule{1.0em}{0ex}}x\in \left(0,{x}_{0}\right]$ is considered, where $p$, $q\in {C}^{1}\left(0,{x}_{0}\right]$, $p\left(x\right)>0$, $q\left(x\right)>0$ for $x\in \left(0,{x}_{0}\right]$. Sufficient conditions are established for every nontrivial solutions to be nonrectifiable oscillatory near $x=0$ without the Hartman–Wintner condition.

## How to cite

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Kanemitsu, Takanao, and Tanaka, Satoshi. "Nonrectifiable oscillatory solutions of second order linear differential equations." Archivum Mathematicum 053.4 (2017): 193-201. <http://eudml.org/doc/294211>.

@article{Kanemitsu2017,
abstract = {The second order linear differential equation \begin\{equation*\} (p(x)y^\{\prime \})^\{\prime \}+q(x)y=0\,, \quad x \in (0,x\_0] \end\{equation*\} 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.},
author = {Kanemitsu, Takanao, Tanaka, Satoshi},
journal = {Archivum Mathematicum},
keywords = {oscillatory; nonrectifiable; second order linear differential equation},
language = {eng},
number = {4},
pages = {193-201},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Nonrectifiable oscillatory solutions of second order linear differential equations},
url = {http://eudml.org/doc/294211},
volume = {053},
year = {2017},
}

TY - JOUR
AU - Kanemitsu, Takanao
AU - Tanaka, Satoshi
TI - Nonrectifiable oscillatory solutions of second order linear differential equations
JO - Archivum Mathematicum
PY - 2017
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 053
IS - 4
SP - 193
EP - 201
AB - The second order linear differential equation \begin{equation*} (p(x)y^{\prime })^{\prime }+q(x)y=0\,, \quad x \in (0,x_0] \end{equation*} 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.
LA - eng
KW - oscillatory; nonrectifiable; second order linear differential equation
UR - http://eudml.org/doc/294211
ER -

## References

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