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Oscillation for even-order delay difference equations with unstable type. (English) Zbl 1053.39024

This paper is concerned with even-order delay difference equations with unstable type, which admit a positive unbounded solution. Oscillation criteria for all bounded solutions are also obtained.

MSC:

39A11 Stability of difference equations (MSC2000)
39A12 Discrete version of topics in analysis
Full Text: DOI

References:

[1] Agarwal, R. P., Difference Equations and Inequalities (1999), Marcel Dekker: Marcel Dekker New York · Zbl 0992.39008
[2] Agarwal, R. P.; Grace, Said R.; O’reqan, Donal, Oscillatory Theory for Difference Equations and Functional Differential Equations (2000), Kluwer Academic Publishers: Kluwer Academic Publishers Dordrecht · Zbl 0954.34002
[3] Agarwal, R. P.; Thandapani, E.; Wong, P. J.Y., Oscillation for higher-order neutral difference equations, Appl. Math. Lett., 10, 1, 71-78 (1997) · Zbl 0890.39019
[4] Grzecorczyk, G.; Werbowski, J., Oscillation of solutions of higher-order linear difference equations, Comput. Math. Appl., 42, 711-717 (2001) · Zbl 1006.39011
[5] Lalli, B. S.; Zhang, B. G., On existence of positive solutions and bounded oscillations for neutral difference equations, J. Math. Anal. Appl., 166, 272-287 (1992) · Zbl 0763.39002
[6] Li, B., Discrete oscillations, J. Differ. Equat. Appl., 2, 389-399 (1996) · Zbl 0881.39007
[7] Shen, J. H., On second order neutral delay difference equations with variable coefficients, J. Math. Study, 27, 60-70 (1994) · Zbl 0917.39006
[8] Szmanda, B., Oscillation of solutions of higher order nonlinear difference equations, Bull. Inst. Math. Acad. Sin., 25, 71-78 (1997) · Zbl 0874.39011
[9] Tang, X. H., Bounded oscillation of second-order delay difference equations with unstable form, Comput. Math. Appl., 44, 1147-1156 (2002) · Zbl 1035.39009
[10] Tang, X. H.; Yu, J. S., Oscillation of delay difference equations, Comput. Math. Appl., 37, 7, 11-20 (1999) · Zbl 0937.39012
[11] Tang, X. H.; Yu, J. S., Oscillations of delay difference equations in a critical state, Appl. Math. Lett., 13, 9-15 (2000) · Zbl 0973.39009
[12] Tang, X. H.; Yu, J. S., A Further result on the oscillation of delay difference equations, Comput. Math. Appl., 38, 11-12, 229-237 (1999) · Zbl 0976.39005
[13] Tang, X. H.; Yu, J. S., Oscillation of delay difference equations, Hokkaido Math. J., 29, 213-228 (2000) · Zbl 0958.39015
[14] Tang, X. H.; Zhang, R. Y., New oscillation criteria for delay difference equations, Comput. Math. Appl., 42, 1319-1330 (2001) · Zbl 1002.39022
[15] Wyrwinska, A., Oscillation criteria of higher-order linear difference equations, Bull. Inst. Math. Acad. Sin., 22, 259-266 (1994) · Zbl 0813.39004
[16] Yu, J. S.; Zhang, B. G.; Qian, X. Z., Oscillation of delay difference equations with oscillating coefficients, J. Math. Anal. Appl., 177, 432-444 (1993) · Zbl 0787.39004
[17] Zhang, G.; Gao, Y., Oscillatory Theory for Difference Equations (2001), Higher Education Press: Higher Education Press Beijing, in Chinese
[18] Zhou, Y., Oscillation of solutions of higher-order linear difference equations, Comput. Math. Appl., 42, 323-331 (2001) · Zbl 1003.39003
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