Tian, C. J.; Zhang, B. G. Frequent oscillation of a class of partial difference equations. (English) Zbl 0923.39009 Z. Anal. Anwend. 18, No. 1, 111-130 (1999). 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. Reviewer: Patricia J.Y.Wong (Singapore) Cited in 8 Documents MSC: 39A12 Discrete version of topics in analysis 39A10 Additive difference equations Keywords:partial difference equations; frequent oscillation; frequent positivity PDFBibTeX XMLCite \textit{C. J. Tian} and \textit{B. G. Zhang}, Z. Anal. Anwend. 18, No. 1, 111--130 (1999; Zbl 0923.39009) Full Text: DOI EuDML 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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.