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Frequent oscillation of a class of partial difference equations. (English) Zbl 0923.39009

The authors consider the following partial difference equation \[ A_{m+1,n}+A_{m,n+1}-a_{m,n}A_{m,n}+p_{m,n}A_{m-k,n-\ell}=0 \tag{1} \] where \(k,\ell\) are nonnegative integers, \(\{a_{m,n}\}\) and \(\{p_{m,n}\}\) are real double sequences. Criteria are developed for equation (1) to be frequently oscillatory. Note that if an equation is frequent oscillatory, then it is oscillatory.

MSC:

39A12 Discrete version of topics in analysis
39A10 Additive difference equations
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References:

[1] Agarwal, R. P.: Difference Equations and Inequalities. New York: Marcel Dekker 1992. · Zbl 0925.39001
[2] Cheng, S. S. and B. G.Zhang: Qualitative theory of partial difference equations. Part I: Oscillation of nonlinear partial difference equations. Tamkang J. Math. 25 (1994), 279 -288. · Zbl 0809.39002
[3] Courant, R., Friedrichs, K. and H. Lewy: On partial difference equations of mathematical physics. IBM J. 11(1967), 215 - 234. · Zbl 0145.40402
[4] Kelley, W. C. and A. C. Peterson: Difference Equations. New York: Acad. Press 1991. · Zbl 0733.39001
[5] Li, X.-P.: Partial difference equations used in the study of molecular orbits (in Chinese). Acta Chimica SINICA 40 (1982), 688 - 698.
[6] Tian, C. J., Xie, S. L. and S. S. Cheng: Measures for oscillatory sequences. Comp. Math. App!. (to appear). · Zbl 0933.39024
[7] Tramov, M. I.: Oscillation of partial diffferential equations with deviating arguments (in Russian). Duff. Uravn. 20 (1984), 721 - 723. · Zbl 0598.35123
[8] Zhang, B. G. and S. T. Liu: On the oscillation of two partial difference equations. J. Math. Anal. App!. 206 (1997), 480 - 492. · Zbl 0877.39012
[9] Zhang, B. C., Liu, S. T. and S. S. Cheng: Oscillation of a class of delay partial difference equations. J. Difference Equ. App!. 1 (1995), 215 - 226. · Zbl 0856.39015
[10] Zhang, B. G. and J. S. Yu: Linearized oscillation theorems for certain nonlinear delay partial difference equations. Comp. Math. Applic. 35 (1998)4, 111 - 116. · Zbl 0907.39017
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