Asymptotic Properties of Solutions of Neutral Type Difference System with Delays

Abstract

We consider a three-dimensional nonlinear difference system with deviating arguments of the following form

$$ \left\{ {\begin{array}{lll} \Delta \left( {x_n + p_n x_n - \tau } \right) = a_n f\left( {y_n - 1} \right) \hfill \cr \qquad\qquad\Delta y_n = b_n g\left( {w_{n - m} } \right), \hfill \cr \qquad\qquad\,\,\,\Delta w_n = \delta c_n h\left( {x_{n - k} } \right) \hfill \cr \end{array}} \right. $$

where the first equation of the system is a neutral type difference equation. First, the classification of nonoscillatory solutions of the considered system is presented. Next, we present the sufficient conditions for boundedness of a nonoscillatory solution. The obtained results are illustrated by examples.

Mathematics Subject Classification (2010). 39A10, 39A11, 39A12.