Geodesic
Iterated oscillation criteria for delay partial difference equations
Mathematica Bohemica, Tome 139 (2014) no. 3, pp. 437-450

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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.
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.
DOI : 10.21136/MB.2014.143934
Classification : 39A14, 39A21
Keywords: partial difference equation; oscillation; variable coefficient 
Karpuz, Başak; Öcalan, Özkan. Iterated oscillation criteria for delay partial difference equations. Mathematica Bohemica, Tome 139 (2014) no. 3, pp. 437-450. doi: 10.21136/MB.2014.143934
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[1] Cheng, S. S.: Partial Difference Equations. Advances in Discrete Mathematics and Applications 3 Taylor and Francis, London (2003). | MR | Zbl

[2] Karpuz, B., Öcalan, Ö.: Further oscillation criteria for partial difference equations with variable coefficients. Comput. Math. Appl. 59 (2010), 55-63. | DOI | MR | Zbl

[3] Zhang, B. G., Agarwal, R. P.: The oscillation and stability of delay partial difference equations. Comput. Math. Appl. 45 (2003), 1253-1295. | DOI | MR | Zbl

[4] Zhang, B. G., Liu, S. T.: On the oscillation of two partial difference equations. J. Math. Anal. Appl. 206 (1997), 480-492. | DOI | MR | Zbl

[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. | DOI | MR | Zbl

[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). | MR | Zbl

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