Asymptotic behavior of oscillatory solutions of first order functional delay difference equations

摘要

In this paper, we study the asymptotic behavior of oscillatory solutions of the first order functional delay difference equation egin{equation*} quad quad quad quad quad quadquad quad quad Delta x(n)=f(n, x(n-au)),quad ngeq n_0. quad quad quad quad quad quad quad quad quadquad quad quad quad quad quadquad quad quadquad quad (*)end{equation*} A new sufficient condition is established under which every oscillatory solution of (*) tends to zero asymptotically.