2018
Том 70
№ 9

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

Abstract

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 present an example of application of abstract results to partial differential equations.

Citation Example: Gefter S. L., Piven’ A. L. Entire solutions of one linear implicit differential-difference equation in Banach spaces // Ukr. Mat. Zh. - 2018. - 70, № 8. - pp. 1044-1057.