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

## DOI:

https://doi.org/10.14419/ijamr.v4i2.4234## Published:

2015-03-08## Keywords:

Asymptotic behavior, Delay difference equation, Oscillatory solution.## Abstract

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 \Delta x(n)=f(n, x(n-\tau)),\quad n\geq 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.

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