# Iterated oscillation criteria for delay partial difference equations

Mathematica Bohemica (2014)

- Volume: 139, Issue: 3, page 437-450
- ISSN: 0862-7959

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topKarpuz, Başak, and Öcalan, Özkan. "Iterated oscillation criteria for delay partial difference equations." Mathematica Bohemica 139.3 (2014): 437-450. <http://eudml.org/doc/262002>.

@article{Karpuz2014,

abstract = {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.},

author = {Karpuz, Başak, Öcalan, Özkan},

journal = {Mathematica Bohemica},

keywords = {partial difference equation; oscillation; variable coefficient; oscillation criterion; linear partial difference equation},

language = {eng},

number = {3},

pages = {437-450},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {Iterated oscillation criteria for delay partial difference equations},

url = {http://eudml.org/doc/262002},

volume = {139},

year = {2014},

}

TY - JOUR

AU - Karpuz, Başak

AU - Öcalan, Özkan

TI - Iterated oscillation criteria for delay partial difference equations

JO - Mathematica Bohemica

PY - 2014

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 139

IS - 3

SP - 437

EP - 450

AB - 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.

LA - eng

KW - partial difference equation; oscillation; variable coefficient; oscillation criterion; linear partial difference equation

UR - http://eudml.org/doc/262002

ER -

## References

top- Cheng, S. S., Partial Difference Equations, Advances in Discrete Mathematics and Applications 3 Taylor and Francis, London (2003). (2003) Zbl1016.39001MR2193620
- Karpuz, B., Öcalan, Ö., 10.1016/j.camwa.2009.09.005, Comput. Math. Appl. 59 (2010), 55-63. (2010) Zbl1189.39011MR2575491DOI10.1016/j.camwa.2009.09.005
- Zhang, B. G., Agarwal, R. P., 10.1016/S0898-1221(03)00099-3, Comput. Math. Appl. 45 (2003), 1253-1295. (2003) Zbl1062.39011MR2000596DOI10.1016/S0898-1221(03)00099-3
- Zhang, B. G., Liu, S. T., 10.1006/jmaa.1997.5239, J. Math. Anal. Appl. 206 (1997), 480-492. (1997) Zbl0877.39012MR1433951DOI10.1006/jmaa.1997.5239
- Zhang, B. G., Liu, S. T., Cheng, S. S., 10.1080/10236199508808022, J. Difference Equ. Appl. 1 (1995), 215-226. (1995) Zbl0856.39015MR1350439DOI10.1080/10236199508808022
- Zhang, B. G., Zhou, Y., Qualitative Analysis of Delay Partial Difference Equations, Contemporary Mathematics and Its Applications 4 Hindawi Publishing Corporation, New York (2007). (2007) Zbl1153.35078MR2388616

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