Geodesic
Solutions to conjectures on a nonlinear recursive equation
Czechoslovak Mathematical Journal, Tome 70 (2020) no. 3, pp. 867-880
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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.
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.
DOI : 10.21136/CMJ.2020.0572-18
Classification : 11B39, 39A10, 39A21
Keywords: recursive equation; nonlinear difference equation; equilibrium point; stability 
@article{10_21136_CMJ_2020_0572_18,
     author = {\"Ocalan, \"Ozkan and Duman, Oktay},
     title = {Solutions to conjectures on a nonlinear recursive equation},
     journal = {Czechoslovak Mathematical Journal},
     pages = {867--880},
     year = {2020},
     volume = {70},
     number = {3},
     doi = {10.21136/CMJ.2020.0572-18},
     mrnumber = {4151710},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2020.0572-18/}
}
TY  - JOUR
AU  - Öcalan, Özkan
AU  - Duman, Oktay
TI  - Solutions to conjectures on a nonlinear recursive equation
JO  - Czechoslovak Mathematical Journal
PY  - 2020
SP  - 867
EP  - 880
VL  - 70
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2020.0572-18/
DO  - 10.21136/CMJ.2020.0572-18
LA  - en
ID  - 10_21136_CMJ_2020_0572_18
ER  - 
%0 Journal Article
%A Öcalan, Özkan
%A Duman, Oktay
%T Solutions to conjectures on a nonlinear recursive equation
%J Czechoslovak Mathematical Journal
%D 2020
%P 867-880
%V 70
%N 3
%U http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2020.0572-18/
%R 10.21136/CMJ.2020.0572-18
%G en
%F 10_21136_CMJ_2020_0572_18
Öcalan, Özkan; Duman, Oktay. Solutions to conjectures on a nonlinear recursive equation. Czechoslovak Mathematical Journal, Tome 70 (2020) no. 3, pp. 867-880. doi: 10.21136/CMJ.2020.0572-18

[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. | DOI | MR | JFM

[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. | DOI | MR | JFM

Cité par Sources :