Global attractivity of a higher order nonlinear difference equation with decreasing terms
In the present paper, we further study the asymptotical behavior of the following higher order nonlinear difference equation \begin{equation*} x(n+1)= ax(n)+ bf( x(n)) + cf(x(n-k)), \qquad n=0, 1, \dots \end{equation*} where $a, b $ and $c$ are constants with $0<a<1, 0\leq b<1, 0\leq c <...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
University of Szeged
2024-03-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
| Subjects: | |
| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=10913 |
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| Summary: | In the present paper, we further study the asymptotical behavior of the following higher order nonlinear difference equation
\begin{equation*}
x(n+1)= ax(n)+ bf( x(n)) + cf(x(n-k)), \qquad n=0, 1, \dots
\end{equation*}
where $a, b $ and $c$ are constants with $0<a<1, 0\leq b<1, 0\leq c <1$ and $a+b+c=1$, $f\in C[[0, \infty), [0, \infty)] $ with $f(x)>0$ for $x>0$, and $k$ is a positive integer, which has been recently studied in: On global attractivity of a higher order difference equation and its applications [Electron. J. Qual. Theory Diff. Equ. 2022, No. 2, 1–14]. We obtain some new sufficient conditions for the global attractivity of positive solutions of the equation, and show the applications of these results to some population models. |
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| ISSN: | 1417-3875 |