Language:   Search:   Contact
Zentralblatt MATH has released its new interface!
For an improved author identification, see the new author database of ZBMATH.

Query:
Fill in the form and click »Search«...
Format:
Display: entries per page entries
Zbl 1172.34025
Pasic, Mervan
Rectifiable and unrectifiable oscillations for a generalization of the Riemann-Weber version of Euler differential equation.
(English)
[J] Georgian Math. J. 15, No. 4, 759-774 (2008). ISSN 1072-947X; ISSN 1572-9176/e

The following generalization $$y''+\frac{1}{x^{\alpha}}\left\{ \frac{1}{4}+\frac{\lambda}{|\ln x|^{\beta}}\right\} y=0 \text{ on }(0,b), \quad b\in (0,1), \ \alpha\geq 2, \ \beta>0, \ \lambda >0$$ of the Riemann-Weber version of the Euler differential equation is introduced and considered with a suitable boundary layer condition depending on $\alpha$ near $x=0$. It is shown that this problem is rectifiable (resp., unrectifiable) oscillatory on $(0,b)$ provided $\alpha\in [2,4)$ (resp., $\alpha\geq 4$).
[Qiru Wang (Guangzhou)]
MSC 2000:
*34C10 Qualitative theory of oscillations of ODE: Zeros, etc.
34A30 Linear ODE and systems

Keywords: Riemann-Weber version of Euler equation; rectifiable oscillation; unrectifiable oscillation; Sturm's comparison principle

Highlights
Master Server