| Title:
|
Conditional oscillation of half-linear differential equations with periodic coefficients (English) |
| Author:
|
Hasil, Petr |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
44 |
| Issue:
|
2 |
| Year:
|
2008 |
| Pages:
|
119-131 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We show that the half-linear differential equation
\[ \big [r(t)\Phi (x^{\prime })\big ]^{\prime } + \frac{s(t)}{t^p} \Phi (x) = 0 \ast \]
with $\alpha $-periodic positive functions $r, s$ is conditionally oscillatory, i.e., there exists a constant $K>0$ such that () with $\frac{\gamma s(t)}{t^p}$ instead of $\frac{s(t)}{t^p}$ is oscillatory for $\gamma > K$ and nonoscillatory for $\gamma < K$. (English) |
| Keyword:
|
oscillation theory |
| Keyword:
|
conditional oscillation |
| Keyword:
|
half-linear differential equations |
| MSC:
|
34C10 |
| idZBL:
|
Zbl 1212.34110 |
| idMR:
|
MR2432849 |
| . |
| Date available:
|
2008-07-24T13:17:52Z |
| Last updated:
|
2013-09-19 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/116929 |
| . |
| Reference:
|
[1] Došlý, O., Řehák, P.: Half-Linear Differential Equations.Elsevier, Mathematics Studies 202, 2005. Zbl 1090.34001, MR 2158903 |
| Reference:
|
[2] Schmidt, K. M.: Oscillation of the perturbed Hill equation and the lower spectrum of radially periodic Schrödinger operators in the plane.Proc. Amer. Math. Soc. 127 (1999), 2367–2374. Zbl 0918.34039, MR 1626474, 10.1090/S0002-9939-99-05069-8 |
| . |
