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 $$x^{(m)}(t) + A_1x^{(m-1)}(t) + ... + A_{m-1}x'(t)) = Ax(t) +f(0), t \in R$$ 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.