Xie, Sheng Li; Tian, Chuan Jun Frequent oscillatory criteria for partial difference equations with several delays. (English) Zbl 1068.39028 Comput. Math. Appl. 48, No. 3-4, 335-345 (2004). A class of unforced partial difference equations with several discrete delays is considered. Solutions are classified according to whether or not they tend to a sign-definite steady state value. Eventually sign-indefinite solutions are labeled as oscillatory. Sufficient conditions are presented for the existence of oscillatory solutions of this class of equations. Reviewer: Edwin Engin Yaz (Milwaukee) Cited in 1 Document MSC: 39A11 Stability of difference equations (MSC2000) 39A12 Discrete version of topics in analysis 35R10 Partial functional-differential equations Keywords:stability; asymptotics; periodic solutions; oscillation; partial difference equations with several discrete delays PDFBibTeX XMLCite \textit{S. L. Xie} and \textit{C. J. Tian}, Comput. Math. Appl. 48, No. 3--4, 335--345 (2004; Zbl 1068.39028) Full Text: DOI References: [1] Zhang, B. G.; Liu, S. T., On the oscillation of two partial difference equations, J. Math. Anal. Appl., 206, 480-492 (1997) · Zbl 0877.39012 [2] Tian, C. J.; Xie, S. L.; Cheng, S. S., Measures for oscillatory sequences, Computers Math. Applic., 36, 10-12, 149-161 (1998) · Zbl 0933.39024 [3] Tian, C. J.; Zhang, B. G., Frequent oscillation of a class of partial difference equations, Zeitschrift fur Analysis and ihre Anwendungen (J. Anal. Appl.), 18, 1, 111-130 (1999) · Zbl 0923.39009 [4] Agarwal, R. P., Difference Equations and Inequalities, Second Edition, Revised and Expanded: Theory, Methods and Applications (1992), Marcel Dekker [5] Zhang, B. G.; Liu, S. T.; Cheng, S. S., Oscillation of a class of delay partial difference equations, J. Difference Equations and its Applications, 1, 215-226 (1995) · Zbl 0856.39015 [6] Zhang, B. G.; Liu, S. T., Oscillation of partial difference equations, Pan American Math. J., 5, 2, 61-70 (1995) · Zbl 0840.39004 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.