2018
Том 70
№ 9

All Issues

Gefter S. L.

Articles: 1
Article (Ukrainian)

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

Gefter S. L., Piven’ A. L.

↓ Abstract

Ukr. Mat. Zh. - 2018. - 70, № 8. - pp. 1044-1057

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.