Nonlinear Oscillations

, Volume 9, Issue 1, pp 1–12 | Cite as

Bounded solutions of linear differential equations in a banach space

  • A. A. Boichuk
  • A. A. Pokutnii


For a linear inhomogeneous differential equation in a Banach space, we find a criterion for the existence of solutions that are bounded on the entire real axis under the assumption that the homogeneous equation admits an exponential dichotomy on the semiaxes. This result is a generalization of the Palmer lemma to the case of infinite-dimensional spaces. We consider examples of countable systems of ordinary differential equations that have bounded solutions.


Banach Space Linear Differential Equation Singular Integral Operator Solvability Condition Bounded Solution 
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Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • A. A. Boichuk
    • 1
  • A. A. Pokutnii
    • 2
  1. 1.Institute of MathematicsUkrainian Academy of SciencesKiev
  2. 2.Shevchenko Kiev National UniversityKiev

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