| Title:
|
Oscillatory properties of second order half-linear difference equations (English) |
| Author:
|
Řehák, Pavel |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
51 |
| Issue:
|
2 |
| Year:
|
2001 |
| Pages:
|
303-321 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We study oscillatory properties of the second order half-linear difference equation \[ \Delta (r_k|\Delta y_k|^{\alpha -2}\Delta y_k)-p_k|y_{k+1}|^{\alpha -2}y_{k+1}=0, \quad \alpha >1. \qquad \mathrm{(HL)}\] It will be shown that the basic facts of oscillation theory for this equation are essentially the same as those for the linear equation \[ \Delta (r_k\Delta y_k)-p_ky_{k+1}=0. \] We present here the Picone type identity, Reid Roundabout Theorem and Sturmian theory for equation (HL). Some oscillation criteria are also given. (English) |
| Keyword:
|
half-linear difference equation |
| Keyword:
|
Picone identity |
| Keyword:
|
Reid Roundabout Theorem |
| Keyword:
|
oscillation criteria |
| MSC:
|
39A10 |
| MSC:
|
39A11 |
| idZBL:
|
Zbl 0982.39004 |
| idMR:
|
MR1844312 |
| . |
| Date available:
|
2009-09-24T10:42:38Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127649 |
| . |
| Reference:
|
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| Reference:
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| . |
