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Zbl 1182.34049
Wong, James S.W.
On rectifiable oscillation of Euler type second order linear differential equations.
(English)
[J] Electron. J. Qual. Theory Differ. Equ. 2007, Paper No. 20, 12 p., electronic only (2007). ISSN 1417-3875/e

Summary: We study the oscillatory behavior of solutions of the second order linear differential equation of Euler type: $$y'' + \lambda x^{-\alpha} y = 0, \ x \in (0, 1],\tag E$$ where $\lambda > 0$ and $\alpha> 2$. Theorem (a) For $2 \le \alpha < 4$, all solution curves of $(E)$ have finite arc length; (b) For $\alpha \ge 4$, all solution curves of $(E)$ have infinite arc length. This answers an open problem posed by M. Pasic.
MSC 2000:
*34C10 Qualitative theory of oscillations of ODE: Zeros, etc.
34A30 Linear ODE and systems

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