Stability problem of some nonlinear difference equations
In this paper, we investigate the asymptotic stability of the recursive sequence xn+1=α+βxn21+γxn−1, n=0,1,… and the existence of certain monotonic solutions of the equation xn+1=xnpf(xn,xn−1,…,xn−k), n=0,1,… which includes as a special case the rational recursive sequence xn+1=βxnp1+∑i=1kγix...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1998-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171298000453 |
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| _version_ | 1832563006014226432 |
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| author | Alaa E. Hamza M. A. El-Sayed |
| author_facet | Alaa E. Hamza M. A. El-Sayed |
| author_sort | Alaa E. Hamza |
| collection | DOAJ |
| description | In this paper, we investigate the asymptotic stability of the recursive sequence
xn+1=α+βxn21+γxn−1, n=0,1,…
and the existence of certain monotonic solutions of the equation
xn+1=xnpf(xn,xn−1,…,xn−k), n=0,1,…
which includes as a special case the rational recursive sequence
xn+1=βxnp1+∑i=1kγixn−1p−r,
where α≥0,β>0,γ>0,γi≥0, i=1,2,…,k,∑i=1kγi>0, p∈{2,3,…}
and r∈{1,2,…,p−1}.
The case when r=0
has been investigated by Camouzis et. al. [1], and for r=0
and p=2 by Camouzis et. al. [2]. |
| format | Article |
| id | doaj-art-3b34624a279a4bec9e90bbc074876bab |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1998-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-3b34624a279a4bec9e90bbc074876bab2025-02-03T01:21:16ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251998-01-0121233134010.1155/S0161171298000453Stability problem of some nonlinear difference equationsAlaa E. Hamza0M. A. El-Sayed1Department of Mathematics, Faculty of Science, Cairo University, Giza 12211, EgyptDepartment of Mathematics, Faculty of Science, Cairo University, Giza 12211, EgyptIn this paper, we investigate the asymptotic stability of the recursive sequence xn+1=α+βxn21+γxn−1, n=0,1,… and the existence of certain monotonic solutions of the equation xn+1=xnpf(xn,xn−1,…,xn−k), n=0,1,… which includes as a special case the rational recursive sequence xn+1=βxnp1+∑i=1kγixn−1p−r, where α≥0,β>0,γ>0,γi≥0, i=1,2,…,k,∑i=1kγi>0, p∈{2,3,…} and r∈{1,2,…,p−1}. The case when r=0 has been investigated by Camouzis et. al. [1], and for r=0 and p=2 by Camouzis et. al. [2].http://dx.doi.org/10.1155/S0161171298000453Difference EquationsMonotonic solutionsstability. |
| spellingShingle | Alaa E. Hamza M. A. El-Sayed Stability problem of some nonlinear difference equations International Journal of Mathematics and Mathematical Sciences Difference Equations Monotonic solutions stability. |
| title | Stability problem of some nonlinear difference equations |
| title_full | Stability problem of some nonlinear difference equations |
| title_fullStr | Stability problem of some nonlinear difference equations |
| title_full_unstemmed | Stability problem of some nonlinear difference equations |
| title_short | Stability problem of some nonlinear difference equations |
| title_sort | stability problem of some nonlinear difference equations |
| topic | Difference Equations Monotonic solutions stability. |
| url | http://dx.doi.org/10.1155/S0161171298000453 |
| work_keys_str_mv | AT alaaehamza stabilityproblemofsomenonlineardifferenceequations AT maelsayed stabilityproblemofsomenonlineardifferenceequations |