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.

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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