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Journal of Mathematical Sciences

, Volume 223, Issue 3, pp 298–304 | Cite as

Boundary-Value Problems for the Lyapunov Equation in Banach Spaces

  • E. V. Panasenko
  • O. O. Pokutnyi
Article
  • 15 Downloads

We propose an approach to the construction of solutions and quasisolutions of a boundary-value problem for the Lyapunov equation in a Banach space. If the necessary and sufficient conditions for the solvability of this boundary-value problem are satisfied, then the corresponding solutions of the problem are constructed by using the generalized inverse operator. As an example, we consider the problem in the space of bounded sequences with countably dimensional matrices.

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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Zaporizhzhya National UniversityZaporizhzhyaUkraine
  2. 2.Institute of MathematicsUkrainian National Academy of SciencesKyivUkraine
  3. 3.Shevchenko Kyiv National University UkraineKyivUkraine

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