|XXXIII Workshop on Geometric Methods in Physics||29.06-5.07.2014|
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Participants of School
Some properties of solution of Volterra difference equations
In many real-life situations, the present state and the manner in which it changes are both dependent on the past. An appropriate model for such situation are discrete Volterra equations, in which the present state depends on the whole previous history. So, Volterra difference equations are widely used for modeling processes in many fields. In our investigation we consider a Volterra difference equation of nonconvolution type in both: scalar and vector cases. We take into consideration this equation under different assumptions on its kernel. The sufficient conditions for existence of solution with required asymptotic properties are obtained. Particularly, we present sufficient conditions under which the considered equation has asymptotically constant solution, asymptotically periodic solution, weighed asymptotically periodic solution and bounded solutions.