Uniqueness of solutions of boundary-value problems for operator-differential equations on a finite segment and on a semiaxis

• Date: 1994
• Main Authors: Radzievskii, G. V., Радзиевский, Г. В.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 1994
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/5761
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

For the equation $L_0x(t)+L_1x′(t) + ... + L_nx^{(n)}(t) = O$, where $L_k, k = 0,1,...,n$, are operators acting in a Banach space, we establish criteria for an arbitrary solution $x(t)$ to be zero provided that the following conditions are satisfied: $x^{(1−1)} (a) = 0, 1 = 1, ..., p$, and $x^{(1−1)...