ASYMPTOTIC-BEHAVIOR OF SOLUTIONS OF FIRST-ORDER NONLINEAR DELAY DIFFERENCE-EQUATIONS

We obtain sufficient conditions which ensure that all solutions of the first order nonlinear delay difference equation Delta y(n) + F(n,y(n- k)) = 0, n is an element of N (n(0)) tend to zero as n --> infinity. I n (E), N(n(0)) = {n(0), n(0) + 1, n(0) + 2,...}, n(0) is a fixed nonne gative integer, k is a nonegative integer, F:N(n(0)) x R --> R is a re al-valued function, and Delta y(n) = y(n+1) - y(n).