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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| Summary: | 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]. |
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| ISSN: | 0161-1712 1687-0425 |