| Title:
|
Solutions to conjectures on a nonlinear recursive equation (English) |
| Author:
|
Öcalan, Özkan |
| Author:
|
Duman, Oktay |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
70 |
| Issue:
|
3 |
| Year:
|
2020 |
| Pages:
|
867-880 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We obtain solutions to some conjectures about the nonlinear difference equation $$ x_{n+1}=\alpha +\beta x_{n-1} {\rm e}^{-x_{n}}, \quad n=0,1,\cdots , \^^M\alpha ,\beta >0. $$ More precisely, we get not only a condition under which the equilibrium point of the above equation is globally asymptotically stable but also a condition under which the above equation has a unique positive cycle of prime period two. We also prove some further results. (English) |
| Keyword:
|
recursive equation |
| Keyword:
|
nonlinear difference equation |
| Keyword:
|
equilibrium point |
| Keyword:
|
stability |
| MSC:
|
11B39 |
| MSC:
|
39A10 |
| MSC:
|
39A21 |
| idZBL:
|
07250694 |
| idMR:
|
MR4151710 |
| DOI:
|
10.21136/CMJ.2020.0572-18 |
| . |
| Date available:
|
2020-09-07T09:41:22Z |
| Last updated:
|
2022-10-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/148333 |
| . |
| Reference:
|
[1] El-Metwally, H., Grove, E. A., Ladas, G., Levins, R., Radin, M.: On the difference equation $x_{n+1}=\alpha +\beta x_{n-1} e^{-x_{n}}$.Nonlinear Anal., Theory Methods Appl. 47 (2001), 4623-4634. Zbl 1042.39506, MR 1975856, 10.1016/S0362-546X(01)00575-2 |
| Reference:
|
[2] Fotiades, N., Papaschinopoulos, G.: Existence, uniqueness and attractivity of prime period two solution for a difference equation of exponential form.Appl. Math. Comput. 218 (2012), 11648-11653. Zbl 1280.39011, MR 2944008, 10.1016/j.amc.2012.05.047 |
| . |
