Geodesic
Solutions to conjectures on a nonlinear recursive equation
Czechoslovak Mathematical Journal, Tome 70 (2020) no. 3, pp. 867-880.

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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 
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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. http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2020.0572-18/

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