| Title:
|
Oscillation of nonlinear three-dimensional difference systems with delays (English) |
| Author:
|
Schmeidel, Ewa |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
135 |
| Issue:
|
2 |
| Year:
|
2010 |
| Pages:
|
163-170 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper the three-dimensional nonlinear difference system $$ \begin{aligned} \Delta x_n&=a_n f(y_{n-l}),\\ \Delta y_n&=b_n g(z_{n-m}),\\ \Delta z_n&=\delta c_n h(x_{n-k}), \end{aligned} $$ is investigated. Sufficient conditions under which the system is oscillatory or almost oscillatory are presented. (English) |
| Keyword:
|
difference equation |
| Keyword:
|
three-dimensional nonlinear system |
| Keyword:
|
oscillation |
| MSC:
|
39A10 |
| idZBL:
|
Zbl 1224.39019 |
| idMR:
|
MR2723083 |
| DOI:
|
10.21136/MB.2010.140693 |
| . |
| Date available:
|
2010-07-20T18:34:14Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140693 |
| . |
| Reference:
|
[1] Agarwal, R. P.: Difference Equations and Inequalities.Theory, Methods, and Applications, Second edition, Monographs and Textbooks in Pure and Applied Mathematics, Marcel Dekker, New York (2000). Zbl 0952.39001, MR 1740241 |
| Reference:
|
[2] Andruch-Sobiło, A., Drozdowicz, A.: Asymptotic behaviour of solutions of third order nonlinear difference equations of neutral type.Math. Bohem. 133 247-258 (2008). Zbl 1199.39022, MR 2494779 |
| Reference:
|
[3] Andruch-Sobiło, A., Migda, M.: On the oscillation of solutions of third order linear difference equations of neutral type.Math. Bohem. 130 19-33 (2005). Zbl 1110.39002, MR 2128356 |
| Reference:
|
[4] Andruch-Sobiło, A., Migda, M.: Bounded solutions of third order nonlinear difference equations.Rocky Mountain J. Math. 36 23-34 (2006). Zbl 1140.39305, MR 2228182, 10.1216/rmjm/1181069486 |
| Reference:
|
[5] Graef, J. R., Thandapani, E.: Oscillation of two-dimensional difference system.Comput. Math. Appl. 38 157-165 (1999). MR 1713170, 10.1016/S0898-1221(99)00246-1 |
| Reference:
|
[6] Kocić, V. L., Ladas, G.: Global Behavior of Nonlinear Difference Equations of Higher Order with Applications.Mathematics and its Applications, Kluwer Academic Publishers Group, Dordrecht (1993). MR 1247956 |
| Reference:
|
[7] Migda, M., Schmeidel, E., Drozdowicz, A.: Nonoscillation results for some third order nonlinear difference equation.Folia Fac. Sci. Natur. Univ. Masaryk. Brun. Math. 13 185-192 (2003). MR 2030436 |
| Reference:
|
[8] Schmeidel, E.: Boundedness of solutions of nonlinear three-dimensional difference systems with delays.Fasc. Math (to appear). MR 2722636 |
| Reference:
|
[9] Schmeidel, E., Zbąszyniak, M.: Asymptotic behavior of solutions of third order difference equation.Proceedings of the International Conference on Difference Equations, Lisbon, 2007 (to appear). |
| Reference:
|
[10] Szafrański, Z., Szmanda, B.: Oscillatory properties of solutions of some difference systems.Rad. Mat. 2 205-214 (1990). MR 1096703 |
| Reference:
|
[11] Thandapani, E., Ponnammal, B.: Oscillatory and asymptotic behavior of solutions of nonlinear two-dimensional difference systems.Math. Sci. Res. Hot-Line 4 1-18 (2000). MR 1731890 |
| Reference:
|
[12] Thandapani, E., Ponnammal, B.: On the oscillation of a nonlinear two-dimensional difference system.Tamkang J. Math. 32 201-209 (2001). Zbl 1009.39009, MR 1853793 |
| Reference:
|
[13] Thandapani, E., Ponnammal, B.: Oscillatory properties of solutions of three dimensional difference systems.Math. Comput. Modelling 42 641-650 (2005). Zbl 1086.39014, MR 2173482, 10.1016/j.mcm.2004.04.010 |
| . |
