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.


39A11 Stability of difference equations (MSC2000)
Full Text: DOI


[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
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.