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Global behavior of solutions of \(x_{n+1}=[\max \{x_n^k,A\}]/x_{n-1}\). (English) Zbl 0895.39004

The aim of the paper is to investigate the boundedness character and the oscillatory properties of solutions of the difference equation in the title, where \(n=1,2,\ldots\), and \(x_0,x_1,A,k \in (0,\infty)\).

MSC:

39A12 Discrete version of topics in analysis
39A10 Additive difference equations
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[1] Janowski, E.J., Kocic, V.L., Ladas, G. and Schultz, S.W. Global behavior of solutions of. Proceedings of the First International Conference on Difference Equations. 1994, San Antonio. Edited by: Elaydi, S.N., Graef, J.R., Ladas, G. and Peterson, A.C. pp.297–310. Gordon and Breach Publishers.
[2] Kocic V.L., Global Asymeptotic Behavior of Nonlinear Difference Equatins of Higher Order with Applications (1993)
[3] Kocic, V.L. and ladas, G. Oscillations of a nonlinear second order difference equation. 1994, San Antonio. Edited by: Elaydi, S.N., Graef, J.R., Ladas, G. and Paterson, A.C. pp.273–282. Gordon and Breach Publishers.
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