Global stability of \(y_{n+1} =\frac {p+qy_{n}+ry_{n-k}}{1+y_{n}}\) (Q861153)

The authors investigate the global asymptotic stability of the unique positive equilibrium and the existence of unbounded solutions for the rational difference equation \[ y_{n+1}=\frac{p+qy_n+ry_{n-k}}{1+y_n},\quad n=0,1,2,\dots \] where the parameters \(p,q,r\) and the initial condition \(y_{-k},\dots,y_{-1},y_0\) are nonnegative, and \(k\in \{1,2,3,\dots\}\).