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A note on the difference equation \(x_{n+1}=\sum_{i=0}^k\tfrac{\alpha_i}{x_{n-1}^{p_i}}\). (English) Zbl 1008.39005

For the difference equation \(x_{n+1}=\sum^k_{i=0} \alpha_ix_{n-i}^{-p_i}\) with positive \(\alpha_i\), \(p_i\) conditions are given concerning the exponents \(p_i\) such that every positive solution lies between positive bounds.

MSC:

39A11 Stability of difference equations (MSC2000)
39B05 General theory of functional equations and inequalities
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References:

[1] Papaschinopoulos G., Equations Appl. 6 (1) pp 75– (2000)
[2] Differ J., Equations Appl. (2002)
[3] DeVault R., Veszprem, Hungary, 1995, in: On the recursive sequence Xn+1 =(A/xpn) + (B/xqn-1), Proceedings of the Second International Conference on Difference Equations (2002)
[4] DeVault R., J. Differ. Equations Appl. 4 (3) pp 259– (1998)
[5] Papaschinopoulos G., J. Differ. Equations Appl. 6 (1) pp 75– (2000) · Zbl 0956.39004 · doi:10.1080/10236190008808214
[6] Papaschinopoulos, G. and Schinas, C.J. ”Errata on the paper ’On the difference equation xn+1=S k-1 i=0(Ai/xpi n-i)+(1/ xpk n-k),”’. · Zbl 0956.39004
[7] Philos Ch.G., Appl. Math. Comput. 62 pp 249– (1994) · Zbl 0817.39005 · doi:10.1016/0096-3003(94)90086-8
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