Geodesic
Nonrectifiable oscillatory solutions of second order linear differential equations
Archivum mathematicum, Tome 53 (2017) no. 4, pp. 193-201
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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.
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.
DOI : 10.5817/AM2017-4-193
Classification : 34C10
Keywords: oscillatory; nonrectifiable; second order linear differential equation 
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Kanemitsu, Takanao; Tanaka, Satoshi. Nonrectifiable oscillatory solutions of second order linear differential equations. Archivum mathematicum, Tome 53 (2017) no. 4, pp. 193-201. doi: 10.5817/AM2017-4-193

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