| Title:
|
Existence and global attractivity of periodic solutions in a higher order difference equation (English) |
| Author:
|
Qian, Chuanxi |
| Author:
|
Smith, Justin |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
54 |
| Issue:
|
2 |
| Year:
|
2018 |
| Pages:
|
91-110 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Consider the following higher order difference equation \begin{equation*} x(n+1)= f\big (n,x(n)\big )+ g\big (n, x(n-k)\big )\,, \quad n=0, 1, \dots \end{equation*} where $f(n,x)$ and $g(n,x)\colon \lbrace 0, 1, \dots \rbrace \times [0, \infty ) \rightarrow [0,\infty )$ are continuous functions in $x$ and periodic functions in $n$ with period $p$, and $k$ is a nonnegative integer. We show the existence of a periodic solution $\lbrace \tilde{x}(n)\rbrace $ under certain conditions, and then establish a sufficient condition for $\lbrace \tilde{x}(n)\rbrace $ to be a global attractor of all nonnegative solutions of the equation. Applications to Riccati difference equation and some other difference equations derived from mathematical biology are also given. (English) |
| Keyword:
|
higher order difference equation |
| Keyword:
|
periodic solution |
| Keyword:
|
global attractivity |
| Keyword:
|
Riccati difference equation |
| Keyword:
|
population model |
| MSC:
|
39A10 |
| MSC:
|
92D25 |
| idZBL:
|
Zbl 06890307 |
| idMR:
|
MR3813737 |
| DOI:
|
10.5817/AM2018-2-91 |
| . |
| Date available:
|
2018-06-05T13:16:06Z |
| Last updated:
|
2020-01-05 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147216 |
| . |
| Reference:
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