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Global attractivity in a nonlinear second-order difference equation. (English) Zbl 0855.39009
The authors obtain a global attractivity result for the positive equilibrium of a nonlinear second order difference equation \(x_{n+1}=f(x_n,x_{n-1})\), \(n=0,1,2,\dots\).
For related results see the monograph of the present authors: Global behavior of nonlinear difference equations of higher order with applications (1993; Zbl 0787.39001).

MSC:
39A11 Stability of difference equations (MSC2000)
39A10 Additive difference equations
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References:
[1] Hutson, Math. Biosci. 111 pp 1– (1992)
[2] Global asymptotic stability of a delay difference equations, Proceedings of the First International Conference on Difference Equations, San Antonio, Texas, May 25–28, 1994, Gordon and Breach, to appear.
[3] and , Global Asymptotic Behavior of Nonlinear Difference Equations of Higher Order with Applications, Kluwer Academic, Dordrecht, 1993. · doi:10.1007/978-94-017-1703-8
[4] Kocic, J. Math. Anal. Appl 173 pp 127– (1993)
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