| Title:
|
Special solutions of linear difference equations with infinite delay (English) |
| Author:
|
Medveď, Milan |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
30 |
| Issue:
|
2 |
| Year:
|
1994 |
| Pages:
|
139-144 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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 $\epsilon \rightarrow 0$. (English) |
| Keyword:
|
difference equation |
| Keyword:
|
infinite delay |
| Keyword:
|
special solution |
| MSC:
|
34K30 |
| MSC:
|
39A10 |
| MSC:
|
39A70 |
| MSC:
|
47B39 |
| idZBL:
|
Zbl 0819.39001 |
| idMR:
|
MR1292565 |
| . |
| Date available:
|
2008-06-06T21:26:06Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107502 |
| . |
| Reference:
|
[1] Medveď, M.: Two-sided solutions of linear integrodifferential equations of Volterra type with delay.Časopis pro pěst. matem. 115 , 3 (1990), 264–272. MR 1071057 |
| Reference:
|
[2] Ryabov, Yu. A.: On the existence of two-sided solutions of linear integrodifferential equations of Volterra type with delay.Čaopis pro pěst. matem. 111, 2 (1986), 26–33. (Russian) MR 0833154 |
| . |
