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Erschienen in:
2015 | OriginalPaper | Buchkapitel
Asymptotic Properties of Solutions of Neutral Type Difference System with Delays
verfasst von : Ewa Schmeidel, Joanna Zonenberg, Barbara Łupińska
Erschienen in: Geometric Methods in Physics
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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.