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Zbl 1131.39009
Stević, Stevo
Existence of nontrivial solutions of a rational difference equation.
(English)
[J] Appl. Math. Lett. 20, No. 1, 28-31 (2007). ISSN 0893-9659

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 {\it 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.
[Lothar Berg (Rostock)]
MSC 2000:
*39A11 Stability of difference equations
39A20 Generalized difference equations

Keywords: Putnam difference equation; global asymptotic stability; equilibrium point; positive solution; nontrivial solutions

Citations: Zbl 0925.39004

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