Approximation of a bounded solution of one difference equation with unbounded operator coefficient by solutions of the corresponding boundary-value problems

We investigate the problem of approximation of a bounded solution of a difference analog of the differential equation Open image in new window by solutions of the corresponding boundary-value problems. Here, A is an unbounded operator in a Banach space B, {A 1,...,A m-1} ⊂L(B) and f:ℝ→B is a fixed function.