On the recursive sequence xn+1=max{c,xnpxn−1p}

This work studies the boundedness and global attractivity for the positive solutions of the difference equation xn+1=max{c,xnpxn−1p},n∈N0, with p,c∈(0,∞)p,c∈(0,∞). It is shown that: (a) there exist unbounded solutions whenever p≥4p≥4, (b) all positive solutions are bounded when p∈(0,4)p∈(0,4), (c) every positive solution is eventually equal to 1 when p∈(0,4)p∈(0,4) and c≥1c≥1, (d) all positive solutions converge to 1 whenever p,c∈(0,1)p,c∈(0,1).