On rectifiable oscillation of Euler type second order linear differential equations
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...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
University of Szeged
2007-10-01
|
| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=279 |
| id |
doaj-5035dc0fa76945d38b79cba2bdb7d5d1 |
|---|---|
| record_format |
Article |
| spelling |
doaj-5035dc0fa76945d38b79cba2bdb7d5d12021-07-14T07:21:19ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38751417-38752007-10-0120072011210.14232/ejqtde.2007.1.20279On rectifiable oscillation of Euler type second order linear differential equationsJames S. W. Wong0The University of Hong Kong, City University of Hong Kong and Chinney Investment Ltd., Hong KongWe 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]http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=279 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
James S. W. Wong |
| spellingShingle |
James S. W. Wong On rectifiable oscillation of Euler type second order linear differential equations Electronic Journal of Qualitative Theory of Differential Equations |
| author_facet |
James S. W. Wong |
| author_sort |
James S. W. Wong |
| title |
On rectifiable oscillation of Euler type second order linear differential equations |
| title_short |
On rectifiable oscillation of Euler type second order linear differential equations |
| title_full |
On rectifiable oscillation of Euler type second order linear differential equations |
| title_fullStr |
On rectifiable oscillation of Euler type second order linear differential equations |
| title_full_unstemmed |
On rectifiable oscillation of Euler type second order linear differential equations |
| title_sort |
on rectifiable oscillation of euler type second order linear differential equations |
| publisher |
University of Szeged |
| series |
Electronic Journal of Qualitative Theory of Differential Equations |
| issn |
1417-3875 1417-3875 |
| publishDate |
2007-10-01 |
| description |
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] |
| url |
http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=279 |
| work_keys_str_mv |
AT jamesswwong onrectifiableoscillationofeulertypesecondorderlineardifferentialequations |
| _version_ |
1721303817578872832 |