| Title:
|
Iterated oscillation criteria for delay partial difference equations (English) |
| Author:
|
Karpuz, Başak |
| Author:
|
Öcalan, Özkan |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
139 |
| Issue:
|
3 |
| Year:
|
2014 |
| Pages:
|
437-450 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper, by using an iterative scheme, we advance the main oscillation result of Zhang and Liu (1997). We not only extend this important result but also drop a superfluous condition even in the noniterated case. Moreover, we present some illustrative examples for which the previous results cannot deliver answers for the oscillation of solutions but with our new efficient test, we can give affirmative answers for the oscillatory behaviour of solutions. For a visual explanation of the examples, we also provide 3D graphics, which are plotted by a mathematical programming language. (English) |
| Keyword:
|
partial difference equation |
| Keyword:
|
oscillation |
| Keyword:
|
variable coefficient |
| MSC:
|
39A14 |
| MSC:
|
39A21 |
| idZBL:
|
Zbl 06391464 |
| idMR:
|
MR3269367 |
| DOI:
|
10.21136/MB.2014.143934 |
| . |
| Date available:
|
2014-09-29T09:07:24Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143934 |
| . |
| Reference:
|
[1] Cheng, S. S.: Partial Difference Equations.Advances in Discrete Mathematics and Applications 3 Taylor and Francis, London (2003). Zbl 1016.39001, MR 2193620 |
| Reference:
|
[2] Karpuz, B., Öcalan, Ö.: Further oscillation criteria for partial difference equations with variable coefficients.Comput. Math. Appl. 59 (2010), 55-63. Zbl 1189.39011, MR 2575491, 10.1016/j.camwa.2009.09.005 |
| Reference:
|
[3] Zhang, B. G., Agarwal, R. P.: The oscillation and stability of delay partial difference equations.Comput. Math. Appl. 45 (2003), 1253-1295. Zbl 1062.39011, MR 2000596, 10.1016/S0898-1221(03)00099-3 |
| Reference:
|
[4] Zhang, B. G., Liu, S. T.: On the oscillation of two partial difference equations.J. Math. Anal. Appl. 206 (1997), 480-492. Zbl 0877.39012, MR 1433951, 10.1006/jmaa.1997.5239 |
| Reference:
|
[5] Zhang, B. G., Liu, S. T., Cheng, S. S.: Oscillation of a class of delay partial difference equations.J. Difference Equ. Appl. 1 (1995), 215-226. Zbl 0856.39015, MR 1350439, 10.1080/10236199508808022 |
| Reference:
|
[6] Zhang, B. G., Zhou, Y.: Qualitative Analysis of Delay Partial Difference Equations.Contemporary Mathematics and Its Applications 4 Hindawi Publishing Corporation, New York (2007). Zbl 1153.35078, MR 2388616 |
| . |
