Global attractivity in a nonlinear difference equation

摘要

We consider the (nonlinear) difference equation xn = a + ∑k=1mbkxn−k, n = 0,1,2… where a and bk (k = 1, 2, …, m) are nonnegative numbers with B ≡ ∑mk = 1bk > 0, and we are interested in whether all positive solutions are attracted by the positive equilibrium L = (a2) + (a2)2 + B.