Special solutions of linear difference equations with infinite delay

Medveď, Milan. "Special solutions of linear difference equations with infinite delay." Archivum Mathematicum 030.2 (1994): 139-144. <http://eudml.org/doc/247547>.

@article{Medveď1994,
abstract = {For the difference equation $(\epsilon )\,\, x_\{n+1\} = Ax_n + \epsilon \sum _\{k = -\infty \}^n R_\{n-k\}x_k$,where $x_n \in Y,\, Y$  is a Banach space, $\epsilon $ is a parameter and  $A$  is a linear, bounded operator. A sufficient condition for the existence of a unique special solution  $y = \lbrace y_n\rbrace _\{n=-\infty \}^\{\infty \}$  passing through the point  $x_0 \in Y$  is proved. This special solution converges to the solution of the equation (0) as  $\epsilon \rightarrow 0$.},
author = {Medveď, Milan},
journal = {Archivum Mathematicum},
keywords = {difference equation; infinite delay; special solution; infinite delay; linear difference equations; Banach space; special solution},
language = {eng},
number = {2},
pages = {139-144},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Special solutions of linear difference equations with infinite delay},
url = {http://eudml.org/doc/247547},
volume = {030},
year = {1994},
}

TY - JOUR
AU - Medveď, Milan
TI - Special solutions of linear difference equations with infinite delay
JO - Archivum Mathematicum
PY - 1994
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 030
IS - 2
SP - 139
EP - 144
AB - For the difference equation $(\epsilon )\,\, x_{n+1} = Ax_n + \epsilon \sum _{k = -\infty }^n R_{n-k}x_k$,where $x_n \in Y,\, Y$  is a Banach space, $\epsilon $ is a parameter and  $A$  is a linear, bounded operator. A sufficient condition for the existence of a unique special solution  $y = \lbrace y_n\rbrace _{n=-\infty }^{\infty }$  passing through the point  $x_0 \in Y$  is proved. This special solution converges to the solution of the equation (0) as  $\epsilon \rightarrow 0$.
LA - eng
KW - difference equation; infinite delay; special solution; infinite delay; linear difference equations; Banach space; special solution
UR - http://eudml.org/doc/247547
ER -