Approximation of a bounded solution of one difference equation with unbounded operator coefficient by solutions of the corresponding boundary-value problems - Gorodnii, M. F.; Romanenko, V. N. (Ukrains’kyi Matematychnyi Zhurnal, 2000)
We investigate the problem of approximation of a bounded solution of a difference analog of the differential equation x^(m)(t) + A_1x^(m-1)(t) + ... + A_m-1x’(t)) = Ax(t) +f(0), t R 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.