On the asymptotically periodic solution of some linear difference equations

Jerzy Popenda; Ewa Schmeidel

Archivum Mathematicum (1999)

  • Volume: 035, Issue: 1, page 13-19
  • ISSN: 0044-8753

Abstract

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For the linear difference equation x n + 1 - a n x n = i = 0 r a n ( i ) x n + i , n N sufficient conditions for the existence of an asymptotically periodic solutions are given.

How to cite

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Popenda, Jerzy, and Schmeidel, Ewa. "On the asymptotically periodic solution of some linear difference equations." Archivum Mathematicum 035.1 (1999): 13-19. <http://eudml.org/doc/248367>.

@article{Popenda1999,
abstract = {For the linear difference equation \[ x\_\{n+1\} -a\_n x\_n = \sum \_\{i=0\}^r a\_n^\{(i)\}x\_\{n+i\}, \;\;\; n \in N \] sufficient conditions for the existence of an asymptotically periodic solutions are given.},
author = {Popenda, Jerzy, Schmeidel, Ewa},
journal = {Archivum Mathematicum},
keywords = {difference equation; asymptotic behaviour; linear difference equation; asymptotic behaviour; periodic solution},
language = {eng},
number = {1},
pages = {13-19},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {On the asymptotically periodic solution of some linear difference equations},
url = {http://eudml.org/doc/248367},
volume = {035},
year = {1999},
}

TY - JOUR
AU - Popenda, Jerzy
AU - Schmeidel, Ewa
TI - On the asymptotically periodic solution of some linear difference equations
JO - Archivum Mathematicum
PY - 1999
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 035
IS - 1
SP - 13
EP - 19
AB - For the linear difference equation \[ x_{n+1} -a_n x_n = \sum _{i=0}^r a_n^{(i)}x_{n+i}, \;\;\; n \in N \] sufficient conditions for the existence of an asymptotically periodic solutions are given.
LA - eng
KW - difference equation; asymptotic behaviour; linear difference equation; asymptotic behaviour; periodic solution
UR - http://eudml.org/doc/248367
ER -

References

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  1. Agarwal R. P., Popenda J., Periodic Solutions of First Order Linear Difference Equations, Math. Comput. Modelling 22, 1, 1995, 11-19. (1995) Zbl0871.39002MR1343651
  2. Musielak R., Popenda J., The Periodic Solutions of the Second Order Nonlinear Difference Equation, Publ. Mat. 32, 1988, 49-56. (1988) Zbl0649.39005MR0939768
  3. Popenda J., Schmeidel E., On the Asymptotic Behavior of Solutions of Linear Difference Equations, Publ. Mat. 38, 1994, 3-9. (1994) Zbl0842.39003MR1291948
  4. Popenda J., Schmeidel E., On the Asymptotic Behaviour of Solution of Some Difference Equations of Infinite Order, (submitted). 

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