The positive solutions of nonautonomous hyperlogistic delay difference equations (Q1767835)

The authors consider the nonautonomous hyperlogistic delay difference equation \[ \Delta x_n=p_n x_n (1-x_{n-k_n})^r, \quad n=0,1,\dots. \] Sufficient conditions are established to guarantee every solution of the equation to be positive. Sufficient conditions are also offered to ensure every positive solution to converge to the equilibrium \(x=1\) of the model, or to oscillate about 1.