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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.

MSC:
39A11 Stability of difference equations (MSC2000)
39A20 Multiplicative and other generalized difference equations, e.g., of Lyness type
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[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)
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