Global attractivity for a nonlinear difference equation with variable delay

摘要

In this paper, we give sufficient conditions under which every solution of the nonlinear difference equation with variable delay x(n + 1) - x(n) + p(n)f(x(g(n))) = 0, n = 0, 1, 2,... tends to zero as n --> infinity. Here, {p(n)} is a nonnegative sequence, f: R --> R is a continuous function with xf(x) > 0 if x not equal 0, and g : N --> Z is nondecreasing and satisfies g(n) less than or equal to n for n greater than or equal to 0 and lim(n-->infinity) g(n) = infinity. (C) 2001 Elsevier Science Ltd. All rights reserved. References: 12