Geodesic
On the rational difference equation $y_{{n+1}}={\frac{\alpha _{{0}}y_{{n}}+\alpha _{{1}}y_{{n-p}}+\alpha _{{2}}y_{{n-q}}+\alpha _{{3}}y_{{n-r}}+\alpha _{{4}}y_{{n-s}}+\alpha _{{5}}y_{{n-t}}}{\beta _{{0}}y_{{n}}+\beta _{{1}}y_{{n-p}}+\beta _{{2}}y_{{n-q}}+\beta _{{3}}y_{{n-r}}+\beta _{{4}}y_{{n-s}}+\beta _{{5}}y_{{n-t}}}}$
El-Moneam, M. A.1 ; Aly, E. S. 1 ; Aiyashi, M. A. 1
1 Mathematics Department, Faculty of Science, Jazan University, Jazan, Kingdom of Saudi Arabia
Journal of nonlinear sciences and its applications, Tome 12 (2019) no. 2, p. 102-119.

Voir la notice de l'article provenant de la source International Scientific Research Publications

In this paper, we examine and explore the boundedness, periodicity, and global stability of the positive solutions of the rational difference equation
$ y_{{n+1}}={\frac{\alpha _{{0}}y_{{n}}+\alpha _{{1}}y_{{n-p}}+\alpha _{{2}}y_{% {n-q}}+\alpha _{{3}}y_{{n-r}}+\alpha _{{4}}y_{{n-s}}+\alpha _{{5}}y_{{n-t}}}{% \beta _{{0}}y_{{n}}+\beta _{{1}}y_{{n-p}}+\beta _{{2}}y_{{n-q}}+\beta _{{3}% }y_{{n-r}}+\beta _{{4}}y_{{n-s}}+\beta _{{5}}y_{{n-t}}}}, $
where the coefficients ${ \alpha _{i},\beta _{i}\in (0,\infty ),\ i=0,1,2,3,4,5},$ and $p,q,r,s,$ and $t$ are positive integers. The initial conditions $y_{-t} ,$ $\ldots, y_{-s} ,\ldots, y_{-r} ,\ldots, y_{-q} ,\ldots, y_{{% -p}} ,\ldots, y_{-1} , y_{0}$ are arbitrary positive real numbers such that $% p$. Some numerical examples will be given to illustrate our result.
DOI : 10.22436/jnsa.012.02.04
Classification : 39A10, 39A11, 39A99, 34C99
Keywords: Difference equation, boundedness, prime, period two solution, stability

El-Moneam, M. A. 1 ; Aly, E. S.  1 ; Aiyashi, M. A.  1

1 Mathematics Department, Faculty of Science, Jazan University, Jazan, Kingdom of Saudi Arabia 
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El-Moneam, M. A.; Aly, E. S. ; Aiyashi, M. A. . On the rational difference equation \(y_{{n+1}}={\frac{\alpha _{{0}}y_{{n}}+\alpha _{{1}}y_{{n-p}}+\alpha _{{2}}y_{{n-q}}+\alpha _{{3}}y_{{n-r}}+\alpha _{{4}}y_{{n-s}}+\alpha _{{5}}y_{{n-t}}}{\beta _{{0}}y_{{n}}+\beta _{{1}}y_{{n-p}}+\beta _{{2}}y_{{n-q}}+\beta _{{3}}y_{{n-r}}+\beta _{{4}}y_{{n-s}}+\beta _{{5}}y_{{n-t}}}}\). Journal of nonlinear sciences and its applications, Tome 12 (2019) no. 2, p. 102-119. doi : 10.22436/jnsa.012.02.04. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.012.02.04/

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