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Global behavior of a higher order nonlinear difference equation. (English) Zbl 1066.39008
The authors consider the difference equation $$ x_{n+1} = f(x_n,x_{n-k}) $$ for $k>1$ fixed. The function $f(u,v)$ is continuous with respect to both arguments on $(0,\infty)$, decreasing in $u$ and increasing in $v$, with $f(\bar{x},v)/v$ non-increasing in $v$, where $\bar{x}$ is the unique positive equilibrium of the equation. Two kinds of global solutions are considered: oscillatory solutions and semi-cycles. Several results on existence of various global solutions are given, incorporating previous results concerning global behavior of equations that are special cases of the above.

MSC:
39A11Stability of difference equations (MSC2000)
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References:
[1] Ladas, G.: Open problems and conjectures. J. differential equations appl. 1, 317-321 (1995) · Zbl 0860.39018
[2] Ladas, G.: Progress report on xn+1=($\alpha +\beta xn+\gamma $xn - 1)/(A+Bxn+Cxn - 1). J. differential equations appl. 5, 211-215 (1995)
[3] Gibbons, C.; Kulenovic, M. R. S.; Ladas, G.: On the recursive sequence xn+1=($\alpha +\beta $xn - 1)/$(\gamma +xn)$. Math. sci. Res. hot-line 4, 1-11 (2000) · Zbl 1039.39004
[4] Kulenovic, M. R. S.; Ladas, G.; Sizer, W. S.: On the recursive sequence xn+1=($\alpha xn+\beta $xn - 1)/($\gamma xn+\delta $xn - 1). Math. sci. Res. hot-line 2, No. 5, 1-16 (1998)
[5] Feuer, J.; Janowski, E. J.; Ladas, G.: Lyness-type equations in the third quadrant. Nonlinear anal. 30, 1183-1189 (1997) · Zbl 0893.39004
[6] Amleh, A. M.; Grove, E. A.; Ladas, G.; Georgiou, D. A.: On the recursive sequence $xn+1=\alpha +xn - 1/xn$. J. math. Anal. appl. 233, 790-798 (1999) · Zbl 0962.39004
[7] Kocic, V. L.; Ladas, G.: Global attractivity in a nonlinear second-order difference equation. Comm. pure appl. Math. 48, 1115-1122 (1995) · Zbl 0855.39009
[8] Kocic, V. L.; Ladas, G.: Global behavior of nonlinear difference equations of higher order with applications. (1993) · Zbl 0787.39001
[9] Devault, R.; Kosmala, W.; Ladas, G.; Schultz, S. W.: Global behavior of yn+1=(p+yn - k)/(qyn+yn - k). Nonlinear anal. 47, 4743-4751 (2001) · Zbl 1042.39523