Oscillation of nonlinear three-dimensional difference systems with delays

Ewa Schmeidel

Mathematica Bohemica (2010)

  • Volume: 135, Issue: 2, page 163-170
  • ISSN: 0862-7959

Abstract

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In this paper the three-dimensional nonlinear difference system Δ x n = a n f ( y n - l ) , Δ y n = b n g ( z n - m ) , Δ z n = δ c n h ( x n - k ) , is investigated. Sufficient conditions under which the system is oscillatory or almost oscillatory are presented.

How to cite

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Schmeidel, Ewa. "Oscillation of nonlinear three-dimensional difference systems with delays." Mathematica Bohemica 135.2 (2010): 163-170. <http://eudml.org/doc/38120>.

@article{Schmeidel2010,
abstract = {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.},
author = {Schmeidel, Ewa},
journal = {Mathematica Bohemica},
keywords = {difference equation; three-dimensional nonlinear system; oscillation; three-dimensional nonlinear difference system},
language = {eng},
number = {2},
pages = {163-170},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Oscillation of nonlinear three-dimensional difference systems with delays},
url = {http://eudml.org/doc/38120},
volume = {135},
year = {2010},
}

TY - JOUR
AU - Schmeidel, Ewa
TI - Oscillation of nonlinear three-dimensional difference systems with delays
JO - Mathematica Bohemica
PY - 2010
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 135
IS - 2
SP - 163
EP - 170
AB - 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.
LA - eng
KW - difference equation; three-dimensional nonlinear system; oscillation; three-dimensional nonlinear difference system
UR - http://eudml.org/doc/38120
ER -

References

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  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). (2008) Zbl1199.39022MR2494779
  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). (2005) Zbl1110.39002MR2128356
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  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). (1993) MR1247956
  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). (2003) MR2030436
  8. Schmeidel, E., Boundedness of solutions of nonlinear three-dimensional difference systems with delays, Fasc. Math (to appear). MR2722636
  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). 
  10. Szafrański, Z., Szmanda, B., Oscillatory properties of solutions of some difference systems, Rad. Mat. 2 205-214 (1990). (1990) MR1096703
  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). (2000) MR1731890
  12. Thandapani, E., Ponnammal, B., On the oscillation of a nonlinear two-dimensional difference system, Tamkang J. Math. 32 201-209 (2001). (2001) Zbl1009.39009MR1853793
  13. Thandapani, E., Ponnammal, B., 10.1016/j.mcm.2004.04.010, Math. Comput. Modelling 42 641-650 (2005). (2005) Zbl1086.39014MR2173482DOI10.1016/j.mcm.2004.04.010

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