Entire solutions of one linear implicit differential-difference equation in Banach spaces

• Date: 2018
• Main Authors: Gefter, S. L., Piven’, A. L., Гефтер, С. Л., Півень, О. Л.
• Format: Article
• Language: Ukrainian
• Published: Institute of Mathematics, NAS of Ukraine 2018
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/1616
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We establish the existence and uniqueness conditions for the solution for the initial problem $Bu\prime (z) = Au(z + h) + f(z),\; z \in C, u(0) = u_0$ in the classes of entire functions of exponential type. Closed linear operators $A$ and $B$ act on Banach spaces and can be degenerate. We also pres...