**On rectifiable oscillation of Euler type second order linear differential equations**

**James S. W. Wong**, City University of Hong Kong, Hong Kong

E. J. Qualitative Theory of Diff. Equ., No. 20. (2007), pp. 1-12.

Communicated by L. Hatvani.
| Received on 2007-04-16 Appeared on 2007-10-08 |

**Abstract: **We study the oscillatory behavior of solutions of the second order linear differential equation of Euler type: $(E)\ y'' + \lambda x^{-\alpha} y = 0, \ x \in (0, 1]$, 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 [8]

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