Slowly Varying Solutions of the Difference Equation Xn+1 = f(Xn,. . ., Xn-k) + g(n, Xn, Xn-1,. . ., Xn-k)

Abstract

We provide conditions which guarantee that all bounded solutions of the difference equation Xn+1 = f(xn, . . ., xn-k) + g(n, xn, xn-1, . . ., xn-k) are slowly varying in the sense that lim(xn+1 - xn) = 0.