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Ukrainian Mathematical Journal

, Volume 70, Issue 8, pp 1205–1220 | Cite as

Entire Solutions of One Linear Implicit Differential-Difference Equation in Banach Spaces

  • S. L. Hefter
  • O. L. Piven’
Article
  • 14 Downloads

We establish the existence and uniqueness conditions for the solution for the initial problem

$$ {Bu}^{\prime }(z)= Au\left(z+h\right)+f(z),\kern1em z\in \mathbb{C},\kern1em u(0)={u}_0 $$

in the classes of entire vector functions of exponential type. Closed linear operators A and B act on Banach spaces and can be degenerate. We present an example of application of abstract results to partial differential equations.

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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • S. L. Hefter
    • 1
  • O. L. Piven’
    • 1
  1. 1.Karazin Kharkiv National UniversityKharkivUkraine

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