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Existence of nontrivial solutions of a rational difference equation. (English) Zbl 1131.39009
The author determines the asymptotic behaviour of a special solution of
\[ x_{n+1}= (x_n+ x_{n-1}+ x_{n-2} x_{n-3})/(x_n x_{n-1}+ x_{n-2}+ x_{n-3}) \] which confirms a conjecture of L. Ladas [J. Difference Equ. Appl. 4, No. 5, 497–499 (1998; Zbl 0925.39004)] concerning the existence of a solution being not eventually constant.

39A11 Stability of difference equations (MSC2000)
39A20 Multiplicative and other generalized difference equations, e.g., of Lyness type
Full Text: DOI
[1] Amleh, A.M.; Kruse, N.; Ladas, G., On a class of difference equations with strong negative feedback, J. difference equ. appl., 5, 6, 497-515, (1999) · Zbl 0951.39002
[2] K. Berenhaut, S. Stević, The global attractivity of a higher order rational difference equation, J. Math. Anal. Appl. (in press)
[3] Berg, L., Asymptotische darstellungen und entwicklungen, (1968), Dt. Verlag Wiss. Berlin · Zbl 0165.36901
[4] Berg, L., On the asymptotics of nonlinear difference equations, Z. anal. anwendungen, 21, 4, 1061-1074, (2002) · Zbl 1030.39006
[5] Berg, L., Inclusion theorems for non-linear difference equations with applications, J. difference equ. appl., 10, 4, 399-408, (2004) · Zbl 1056.39003
[6] Berg, L., Corrections to “inclusion theorems for non-linear difference equations with applications,” from [3], J. difference equ. appl., 11, 2, 181-182, (2005) · Zbl 1080.39002
[7] Berg, L.; Wolfersdorf, L.v., On a class of generalized autoconvolution equations of the third kind, Z. anal. anwendungen, 24, 2, 217-250, (2005) · Zbl 1104.45001
[8] Kruse, N.; Nesemann, T., Global asymptotic stability in some discrete dynamical systems, J. math. anal. appl., 235, 151-158, (1999) · Zbl 0933.37016
[9] Ladas, G., Open problems and conjectures, J. difference equ. appl., 4, 497-499, (1998)
[10] Exam, Putnam, Amer. math. monthly, 734-736, (1965)
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