Geodesic
On entire solutions of exponential type of some implicit linear differential-difference equation in a Banach space
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 41, Tome 416 (2013), pp. 91-97 
S. L. Gefter; T. E. Stulova. On entire solutions of exponential type of some implicit linear differential-difference equation in a Banach space. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 41, Tome 416 (2013), pp. 91-97. http://geodesic.mathdoc.fr/item/ZNSL_2013_416_a3/
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

Let $A$ be a closed linear operator on a Banach space with a possibly domain. Entire solutions of exponential type of the linear differential-difference equation $w'(z)=Aw(z-h)+f(z)$ are studied nondense. Assuming that operator $A$ has a bounded inverse, the well-posedness of this equation in a special space of entire $E$-valued function is proved.

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