Previous |  Up |  Next

# Article

Full entry | PDF   (0.2 MB)
Keywords:
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

Partner of