Global attractivity for a nonlinear difference equation with variable delay

Abstract 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 → ∞. Here, p n is a nonnegative sequence, f : R → R is a continuous function with xf ( x ) > 0 if x ≠ 0, and g : N → Z is nondecreasing and satisfies g ( n ) ≤ n for n ≥ 0 and lim n →∞ g ( n ) = ∞.