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Oscillatory properties of solutions of three-dimensional difference systems. (English) Zbl 1086.39014

The authors obtain some oscillation criteria for the difference system \[ \begin{aligned} \Delta x_n&=a_ny_n^\alpha,\\ \Delta y_n &=b_nz_n^\beta,\\ \Delta z_n&=-c_nx_n^\gamma. \end{aligned} \] Examples are also included.

MSC:

39A11 Stability of difference equations (MSC2000)
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References:

[1] Agarwal, R. P., Difference Equations and Inequalities (2000), Marcel Dekker: Marcel Dekker Cambridge · Zbl 1006.00501
[2] Agarwal, R. P.; Grace, S. R., Oscillation of certain third order difference equations, Computers Math. Applic., 42, 3-5, 379-384 (2001) · Zbl 1003.39006
[3] Graef, J. R.; Thandapani, E., Oscillatory and asymptotic behavior of solutions of third order delay difference equations, Funk. Ekv., 42, 7/8, 355-369 (1999) · Zbl 1141.39301
[4] Smith, B.; Taylor, W. E., Nonlinear third order difference equations: Oscillatory and asymptotic behavior, Tamkang J. Math., 19, 91-95 (1988) · Zbl 0688.39001
[5] Graef, J. R.; Thandapani, E., Oscillation of two-dimensional difference systems, Computers Math. Applic., 38, 7/8, 157-165 (1999) · Zbl 0964.39012
[6] Huo, H. F.; Li, W. T., Oscillation of the Emden-Fowler difference systems, J. Math. Anal. Appl., 256, 478-485 (2001) · Zbl 0976.39003
[7] Li, W. T., Classification schemes for nonoscillatory solutions of two-dimensional nonlinear difference systems, Computers Math. Applic., 42, 3-5, 341-355 (2001) · Zbl 1006.39013
[8] Li, W. T.; Cheng, S. S., Oscillation criteria for a pair of coupled nonlinear difference equations, Internat. J. Appl. Math., 2, 11, 1327-1333 (2000) · Zbl 1051.39006
[9] Szafranski, Z.; Szmanda, B., Oscillatory properties of solutions of some difference systems, Rad. Mat., 6, 205-214 (1990) · Zbl 0762.39007
[10] Hardy, G. H.; Littlewood, J. E.; Polya, G., Inequalities (1988), Cambridge Univ.Press: Cambridge Univ.Press New York · Zbl 0634.26008
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