On the global asymptotic stability of the difference equation xn=xn-1xn-2+xn-3+axn-1+xn-2xn-3+a

摘要

Li and Zhu [Applied Mathematics and Computation, 150 (2004) 481] studied the difference equationxn=xn-1xn-2+xn-3+axn-1+xn-2xn-3+a,n=1,2,…where a ⩾ 0. They claimed that the unique positive equilibrium of the equation is globally asymptotically stable. Unfortunately, there is a subtle mistake in their proof. In this paper, we present a correct proof for this claim.