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Session 7. Difference equations and their application in the mathematical modeling
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Sufficient conditions for existence of bounded solution of nonlinear difference system |
Joanna Zonenberg, Instiute of Mathematics, University of Białystok, Poland,
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The talk is based on the joint work with Ewa Schmeidel and Robert Jankowski with Instiute of Mathematics, University of Białystok, Poland
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We consider three--dimensional nonlinear difference system with deviating arguments on the following form
\begin{eqnarray*}
\left\{
\begin{array}{rl}
\Delta (x_n+px_{n-\tau})&=a_n f(y_{n-l})\\
\Delta y_n&=b_n g(w_{n-m}),\\
\Delta w_n&=\delta c_n h(x_{n-k})
\end{array}
\right.
\end{eqnarray*}
where the first equation of the the system is a neutral type difference equation, \(p\) is a given real constant and \(\delta=\pm 1\). Firstly we present the classification of nonoscillatory solutions of the considered system. Next, we put the sufficient conditions for boundedness of a nonoscillatory solution. At the end we ilustrate the obtained results by example.
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References- R. P. Agarwal, Difference equations and inequalities. Theory, methods and applications ,Marcel Dekker, Inc., New York 1992.
- M. Migda, J. Migda, Asymptotic properties of solutions of second--order neutral difference equations , Nonlinear Anal., 63, e789-e799, (2005).
- E. Schmeidel, Boundedness of solutions of nonlinear three-dimensional difference systems with delays , Fasc. Math., 44, 107--113, (2010).
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