| Title:
|
An oscillatory half-linear differential equation (English) |
| Author:
|
Elbert, Árpád |
| Author:
|
Kusano, Takaŝi |
| Author:
|
Tanigawa, Tomoyuki |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
33 |
| Issue:
|
3 |
| Year:
|
1997 |
| Pages:
|
355-361 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A second-order half-linear ordinary differential equation of the type $$(|y^{\prime}|^{\alpha-1}y^{\prime})^{\prime}+\alpha q(t)|y|^{\alpha-1}y=0 \leqno{{\rm (1)}}$$ is considered on an unbounded interval. A simple oscillation condition for (1) is given in such a way that an explicit asymptotic formula for the distribution of zeros of its solutions can also be established. (English) |
| Keyword:
|
half-linear differential equations |
| MSC:
|
34C10 |
| MSC:
|
35J60 |
| MSC:
|
46F10 |
| idZBL:
|
Zbl 0914.34026 |
| idMR:
|
MR1601353 |
| . |
| Date available:
|
2008-06-06T21:34:48Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107624 |
| . |
| Reference:
|
[1] Elbert Á.: A half-linear second order differential equation.Colloquia Math. Soc. János Bolyai 34: Qualitative Theory of Differential Equation, Szeged (1979), 153 - 180. MR 0680591 |
| Reference:
|
[2] Elbert Á.: Oscillation and nonoscillation theorems for some non-linear ordinary differential equations.Lecture Notes in Mathematics (Springer), Vol. 956 (1982), 187 - 212. MR 0693113 |
| Reference:
|
[3] E. Hille: Lectures on Ordinary Differential Equations.Addison-Wesley, Reading, Massachusetts (1969). Zbl 0179.40301, MR 0249698 |
| Reference:
|
[4] Li H. J., Yeh C. C.: Sturmian comparison theorem for half-linear second order differential equations.Proc. Royal Soc. Edinburgh 125A (1995), 1193 - 1204. Zbl 0873.34020, MR 1362999 |
| Reference:
|
[5] Piros M.: On the solutions of a half-Linear differential equation.Studia Sci. Math. Hungar., 19 (1984), 193 - 211. Zbl 0638.34024, MR 0874484 |
| . |
