Advances in Difference Equations
Volume 2009 (2009), Article ID 784935, 18 pages
Research Article

Construction of the General Solution of Planar Linear Discrete Systems with Constant Coefficients and Weak Delay

1Brno University of Technology, Brno, Czech Republic
2Kiev University, Kiev, Ukraine

Received 19 January 2009; Accepted 30 March 2009

Academic Editor: Ulrich Krause

Copyright © 2009 J. Diblík et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Planar linear discrete systems with constant coefficients and weak delay are considered. The characteristic equations of such systems are identical with those for the same systems but without delayed terms. In this case, the space of solutions with a given starting dimension is pasted after several steps into a space with dimension less than the starting one. In a sense this situation copies an analogous one known from the theory of linear differential systems with constant coefficients and weak delay when the initially infinite dimensional space of solutions on the initial interval on a reduced interval, turns (after several steps) into a finite dimensional set of solutions. For every possible case, general solutions are constructed and, finally, results on the dimensionality of the space of solutions are deduced.