Let A be a closed linear operator on a Banach space E with a possibly nondense domain. Entire solutions of exponential type of the linear differential-difference equation w′(z) = Aw(z−h)+f(z) are studied. Assuming that A has a bounded inverse, the well-posedness of this equation in a special space of entire E-valued functions is proved. Bibliography: 12 titles.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 416, 2013, pp. 91–97.
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Gefter, S., Stulova, T. On Entire Solutions of Exponential Type for Some Implicit Linear Differential-Difference Equation in a Banach Space. J Math Sci 202, 541–545 (2014). https://doi.org/10.1007/s10958-014-2060-3
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DOI: https://doi.org/10.1007/s10958-014-2060-3