an:05218438
Zbl 1131.39009
Stevi??, Stevo
Existence of nontrivial solutions of a rational difference equation
EN
Appl. Math. Lett. 20, No. 1, 28-31 (2007).
00188161
2007
j
39A11 39A20
Putnam difference equation; global asymptotic stability; equilibrium point; positive solution; nontrivial solutions
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 \textit{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)
Zbl 0925.39004