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


Zbl 0925.39004
Full Text: DOI


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