Ukrainian Mathematical Journal

, Volume 56, Issue 11, pp 1766–1781 | Cite as

Criteria for the Well-Posedness of the Cauchy Problem for Differential Operator Equations of Arbitrary Order

  • L. A. Vlasenko
  • A. L. Piven’
  • A. G. Rutkas


In Banach spaces, we investigate the differential equation \(\mathop \sum \nolimits_{j = 0}^n \;A_j u^{(j)} (t) = 0\) with closed linear operators A j (generally speaking, the operator coefficient A n of the higher derivative is degenerate). We obtain well-posedness conditions that characterize the continuous dependence of solutions and their derivatives on initial data. Abstract results are applied to partial differential equations.


Differential Equation Banach Space Partial Differential Equation Initial Data Linear Operator 
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Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • L. A. Vlasenko
    • 1
  • A. L. Piven’
    • 1
  • A. G. Rutkas
    • 1
  1. 1.Kharkov National UniversityKharkovUkraine

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