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Ukrainian Mathematical Journal

, Volume 58, Issue 11, pp 1656–1672 | Cite as

On the correct solvability of the Dirichlet problem for operator differential equations in a Banach space

  • V. M. Horbachuk
  • M. L. Horbachuk
Article
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Abstract

We investigate the structure of solutions of an equation y″(t) = By(t), where B is a weakly positive operator in a Banach space \(\mathfrak{B}\), on the interval (0, ∞) and establish the existence of their limit values as t → 0 in a broader locally convex space containing \(\mathfrak{B}\) as a dense set. The analyticity of these solutions on (0, ∞) is proved and their behavior at infinity is studied. We give conditions for the correct solvability of the Dirichlet problem for this equation and substantiate the applicability of power series to the determination of its approximate solutions.

Keywords

Banach Space Entire Function Vector Function Dirichlet Problem Positive Operator 
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Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • V. M. Horbachuk
    • 1
  • M. L. Horbachuk
    • 2
  1. 1.Kyiv Polytechnic InstituteKyiv
  2. 2.Institute of MathematicsUkrainian Academy of SciencesKyiv

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