Article
Full entry |
PDF
(0.2 MB)
Feedback
PDF
(0.2 MB)
Feedback
Keywords:
difference equation; infinite delay; special solution
difference equation; infinite delay; special solution
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 $\epsilon \rightarrow 0$.
References:
[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
[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
Search
Partner of
