# Unbounded solutions of the max-type difference equation ${x}_{n+1}=max\left\{\frac{{A}_{n}}{{X}_{n}},\frac{{B}_{n}}{{X}_{n-2}}\right\}$

Open Mathematics (2008)

• Volume: 6, Issue: 2, page 307-324
• ISSN: 2391-5455

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## Abstract

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We investigate the boundedness nature of positive solutions of the difference equation ${x}_{n+1}=max\left\{\frac{{A}_{n}}{{X}_{n}},\frac{{B}_{n}}{{X}_{n-2}}\right\},n=0,1,...,$ where A nn=0∞ and B nn=0∞ are periodic sequences of positive real numbers.

## How to cite

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Christopher Kerbert, and Michael Radin. "Unbounded solutions of the max-type difference equation $x_{n + 1} = max\left\lbrace {\frac{{A_n }}{{X_n }},\frac{{B_n }}{{X_{n - 2} }}} \right\rbrace$." Open Mathematics 6.2 (2008): 307-324. <http://eudml.org/doc/269416>.

@article{ChristopherKerbert2008,
abstract = {We investigate the boundedness nature of positive solutions of the difference equation $x\_\{n + 1\} = max\left\lbrace \{\frac\{\{A\_n \}\}\{\{X\_n \}\},\frac\{\{B\_n \}\}\{\{X\_\{n - 2\} \}\}\} \right\rbrace ,n = 0,1,...,$ where A nn=0∞ and B nn=0∞ are periodic sequences of positive real numbers.},
author = {Christopher Kerbert, Michael Radin},
journal = {Open Mathematics},
keywords = {difference equation; unbounded solutions; eventually periodic solution; rational difference equation; eventually periodic solutions; max-type difference equation; positive solutions},
language = {eng},
number = {2},
pages = {307-324},
title = {Unbounded solutions of the max-type difference equation $x\_\{n + 1\} = max\left\lbrace \{\frac\{\{A\_n \}\}\{\{X\_n \}\},\frac\{\{B\_n \}\}\{\{X\_\{n - 2\} \}\}\} \right\rbrace$},
url = {http://eudml.org/doc/269416},
volume = {6},
year = {2008},
}

TY - JOUR
AU - Christopher Kerbert
TI - Unbounded solutions of the max-type difference equation $x_{n + 1} = max\left\lbrace {\frac{{A_n }}{{X_n }},\frac{{B_n }}{{X_{n - 2} }}} \right\rbrace$
JO - Open Mathematics
PY - 2008
VL - 6
IS - 2
SP - 307
EP - 324
AB - We investigate the boundedness nature of positive solutions of the difference equation $x_{n + 1} = max\left\lbrace {\frac{{A_n }}{{X_n }},\frac{{B_n }}{{X_{n - 2} }}} \right\rbrace ,n = 0,1,...,$ where A nn=0∞ and B nn=0∞ are periodic sequences of positive real numbers.
LA - eng
KW - difference equation; unbounded solutions; eventually periodic solution; rational difference equation; eventually periodic solutions; max-type difference equation; positive solutions
UR - http://eudml.org/doc/269416
ER -

## References

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1. [1] Briden W.J., Grove E.A., Kent C.M., Ladas G., Eventually periodic solutions of ${x}_{n+1}=max\left\{\frac{1}{{X}_{n}},\frac{{A}_{n}}{{X}_{n-1}}\right\}$ , Comm. Appl. Nonlinear Anal., 1999, 6, 31–43
2. [2] Briden W.J., Grove E.A., Ladas G., McGrath L.C., On the nonautonomous equation ${x}_{n+1}=max\left\{\frac{{A}_{n}}{{X}_{n}},\frac{{B}_{n}}{{X}_{n-2}}\right\}$ , New developments in difference equations and applications, Proceedings of the Third International Conference on Difference Equations and Applications (1–5 Sept. 1997 Taipei Taiwan), Gordon and Breach, Amsterdam, 1999, 49–73
3. [3] Grove E.A., Kent C.M., Ladas G., Radin M.A., On ${x}_{n+1}=max\left\{\frac{1}{{X}_{n}},\frac{{A}_{n}}{{X}_{n-1}}\right\}$ with a period 3 parameter, Fields Inst. Commun., 2001, 29, 161–180 Zbl0980.39012
4. [4] Kent C.M., Radin M.A., On the boundedness nature of positive solutions of the difference equation ${x}_{n+1}=max\left\{\frac{{A}_{n}}{{X}_{n}},\frac{{B}_{n}}{{X}_{n-2}}\right\}$ with periodic parameters, Proceedings of the Third International DCDIS Conference on Engineering Applications and Computational Algorithms (15 May 2003 Guelph Canada), Dyn. Contin. Discrete Impuls. Syst. Ser. B Appl. Algorithms, 2003, 11–15

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