On the positive solutions of the difference equation \(x_{n+1}=(x_{n-1})/(1+x_{n} x_{n-1})\).
The author obtains the exact expression of the positive solutions of the difference equation \[ x_{n+1}=\frac{x_{n-1}}{1+x_nx_{n-1}}, \quad n=0,1,2,\dots, \] where \(x_{-1}\) and \(x_0\) are two positive real numbers. From this expression it is deduced that the constant solution 0 is the unique equilibrium point.
scientific article; zbMATH DE number 2056325