# Asymptotic properties of solutions of nonautonomous difference equations

Archivum Mathematicum (2010)

- Volume: 046, Issue: 1, page 1-11
- ISSN: 0044-8753

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topMigda, Janusz. "Asymptotic properties of solutions of nonautonomous difference equations." Archivum Mathematicum 046.1 (2010): 1-11. <http://eudml.org/doc/37649>.

@article{Migda2010,

abstract = {Asymptotic properties of solutions of difference equation of the form
\[ \Delta ^m x\_n=a\_n\varphi \_n(x\_\{\sigma (n)\})+b\_n \]
are studied. Conditions under which every (every bounded) solution of the equation $\Delta ^m y_n=b_n$ is asymptotically equivalent to some solution of the above equation are obtained. Moreover, the conditions under which every polynomial sequence of degree less than $m$ is asymptotically equivalent to some solution of the equation and every solution is asymptotically polynomial are obtained. The consequences of the existence of asymptotically polynomial solution are also studied.},

author = {Migda, Janusz},

journal = {Archivum Mathematicum},

keywords = {difference equation; asymptotic behavior; asymptotically polynomial solution; difference equation; asymptotic behavior; asymptotically polynomial solution; Schauder fixed point theorem; sequence spaces},

language = {eng},

number = {1},

pages = {1-11},

publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},

title = {Asymptotic properties of solutions of nonautonomous difference equations},

url = {http://eudml.org/doc/37649},

volume = {046},

year = {2010},

}

TY - JOUR

AU - Migda, Janusz

TI - Asymptotic properties of solutions of nonautonomous difference equations

JO - Archivum Mathematicum

PY - 2010

PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno

VL - 046

IS - 1

SP - 1

EP - 11

AB - Asymptotic properties of solutions of difference equation of the form
\[ \Delta ^m x_n=a_n\varphi _n(x_{\sigma (n)})+b_n \]
are studied. Conditions under which every (every bounded) solution of the equation $\Delta ^m y_n=b_n$ is asymptotically equivalent to some solution of the above equation are obtained. Moreover, the conditions under which every polynomial sequence of degree less than $m$ is asymptotically equivalent to some solution of the equation and every solution is asymptotically polynomial are obtained. The consequences of the existence of asymptotically polynomial solution are also studied.

LA - eng

KW - difference equation; asymptotic behavior; asymptotically polynomial solution; difference equation; asymptotic behavior; asymptotically polynomial solution; Schauder fixed point theorem; sequence spaces

UR - http://eudml.org/doc/37649

ER -

## References

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