Ukrainian Mathematical Journal

, Volume 67, Issue 5, pp 658–667 | Cite as

Fredholm Boundary-Value Problems with Parameter in Sobolev Spaces

  • E. V. Gnyp
  • T. I. Kodlyuk
  • V. A. Mikhailets

For systems of linear differential equations of order r ∈ ℕ, we study the most general class of inhomogeneous boundary-value problems whose solutions belong to the Sobolev space W p n + r ([a, b],ℂ m ), where m, n + 1 ∈ ℕ and p ∈ [1,∞). We show that these problems are Fredholm problems and establish the conditions under which these problems have unique solutions continuous with respect to the parameter in the norm of this Sobolev space.


Banach Space Cauchy Problem Sobolev Space Vector Function Matrix Function 
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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • E. V. Gnyp
    • 1
  • T. I. Kodlyuk
    • 2
  • V. A. Mikhailets
    • 1
    • 3
  1. 1.Institute of MathematicsUkrainian National Academy of SciencesKyivUkraine
  2. 2.Ternopil’ National Pedagogic UniversityTernopil’Ukraine
  3. 3.“Kyiv Polytechnic Institute” Ukrainian National Technical UniversityKyivUkraine

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