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

• Date: 2000
• Main Authors: Gorodnii, M. F., Romanenko, V. N., Городній, М. Ф., Романенко, В. М.
• Format: Article
• Language: Ukrainian; English
• Published: Institute of Mathematics, NAS of Ukraine 2000
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/4445
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

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 i...