Asymptotic behavior of oscillatory solutions of first order functional delay difference equations - Murugesan, A.; Soundara Rajan, C. (International Journal of Applied Mathematical Research, 2015)
In this paper, we study the asymptotic behavior of oscillatory solutions of the first order functional delay difference equation\begin{equation*} \quad \quad \quad \quad \quad \quad\quad \quad \quad Δ x(n)=f(n, x(n-τ)),\quad n≥ n_0. \quad \quad \quad \quad \quad \quad \quad \quad \quad\quad \quad \quad \quad \quad \quad\quad \quad \quad\quad \quad (*)\end{equation*}A new sufficient condition is established under which every oscillatory solution of (*) tends to zero asymptotically.