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Volume 27, Issue 4
$\boldsymbol{Ψ}$-Bounded Solutions for a System of Difference Equations on $\mathbb{Z}$

Yuliang Han, Baifeng Liu & Xidong Sun

Commun. Math. Res., 27 (2011), pp. 331-342.

Published online: 2021-05

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  • Abstract

In this work we discuss the existence of $\boldsymbol{Ψ}$-bounded solutions for linear difference equations. We present a necessary and sufficient condition for the existence of $\boldsymbol{Ψ}$-bounded solutions for the linear nonhomogeneous difference equation $\boldsymbol{x}(n+1) = \boldsymbol{A}(n) \boldsymbol{x}(n) + \boldsymbol{f}(n)$ for every $\boldsymbol{Ψ}$-bounded sequence $\boldsymbol{f}(n)$.

  • Keywords

difference equation, $\boldsymbol{Ψ}$-bounded solution, existence.

  • AMS Subject Headings

39A06, 39A22

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CMR-27-331, author = {Yuliang and Han and and 18420 and and Yuliang Han and Baifeng and Liu and and 18421 and and Baifeng Liu and Xidong and Sun and and 18422 and and Xidong Sun}, title = {$\boldsymbol{Ψ}$-Bounded Solutions for a System of Difference Equations on $\mathbb{Z}$}, journal = {Communications in Mathematical Research }, year = {2021}, volume = {27}, number = {4}, pages = {331--342}, abstract = {

In this work we discuss the existence of $\boldsymbol{Ψ}$-bounded solutions for linear difference equations. We present a necessary and sufficient condition for the existence of $\boldsymbol{Ψ}$-bounded solutions for the linear nonhomogeneous difference equation $\boldsymbol{x}(n+1) = \boldsymbol{A}(n) \boldsymbol{x}(n) + \boldsymbol{f}(n)$ for every $\boldsymbol{Ψ}$-bounded sequence $\boldsymbol{f}(n)$.

}, issn = {2707-8523}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cmr/19077.html} }
TY - JOUR T1 - $\boldsymbol{Ψ}$-Bounded Solutions for a System of Difference Equations on $\mathbb{Z}$ AU - Han , Yuliang AU - Liu , Baifeng AU - Sun , Xidong JO - Communications in Mathematical Research VL - 4 SP - 331 EP - 342 PY - 2021 DA - 2021/05 SN - 27 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/cmr/19077.html KW - difference equation, $\boldsymbol{Ψ}$-bounded solution, existence. AB -

In this work we discuss the existence of $\boldsymbol{Ψ}$-bounded solutions for linear difference equations. We present a necessary and sufficient condition for the existence of $\boldsymbol{Ψ}$-bounded solutions for the linear nonhomogeneous difference equation $\boldsymbol{x}(n+1) = \boldsymbol{A}(n) \boldsymbol{x}(n) + \boldsymbol{f}(n)$ for every $\boldsymbol{Ψ}$-bounded sequence $\boldsymbol{f}(n)$.

Yuliang Han, Baifeng Liu & Xidong Sun. (2021). $\boldsymbol{Ψ}$-Bounded Solutions for a System of Difference Equations on $\mathbb{Z}$. Communications in Mathematical Research . 27 (4). 331-342. doi:
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