Ukrainian Mathematical Journal

, Volume 59, Issue 5, pp 708–717 | Cite as

Phragmén-Lindelöf theorem for solutions of elliptic differential equations in a banach space

  • M. L. Horbachuk


For a second-order elliptic differential equation considered on a semiaxis in a Banach space, we show that if the order of growth of its solution at infinity is not higher than the exponential order, then this solution tends exponentially to zero at infinity.


Banach Space Harmonic Function Vector Function Positive Operator Linear Continuous Operator 
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Copyright information

© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

  • M. L. Horbachuk
    • 1
  1. 1.Institute of MathematicsUkrainian National Academy of SciencesKyiv

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