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On the Solvability of Fredholm Boundary-Value Problems in Fractional Sobolev Spaces

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Ukrainian Mathematical Journal Aims and scope

We study systems of linear ordinary differential equations with the most general inhomogeneous boundary conditions in fractional Sobolev spaces on a finite interval. The Fredholm property of these problems in the corresponding pairs of Banach spaces is proved. Their indices and dimensions of the kernels and cokernels are determined. We also present examples showing the constructive character of the obtained results.

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Authors and Affiliations

  1. Institute of Mathematics of the Czech Academy of Sciences, Prague, Czech Republic

    V. A. Mikhailets & O. M. Atlasiuk

  2. Institute of Mathematics, National Academy of Sciences of Ukraine, Kyiv, Ukraine

    V. A. Mikhailets & O. M. Atlasiuk

  3. “I. Sikorsky Kyiv Polytechnic Institute” Ukrainian National Technical University, Kyiv, Ukraine

    T. B. Skorobohach

Authors
  1. V. A. Mikhailets
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  2. O. M. Atlasiuk
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  3. T. B. Skorobohach
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Correspondence to V. A. Mikhailets.

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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 75, No. 1, pp. 96–104, January, 2023. Ukrainian DOI: https://doi.org/10.37863/umzh.v75i1.7308.

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Mikhailets, V.A., Atlasiuk, O.M. & Skorobohach, T.B. On the Solvability of Fredholm Boundary-Value Problems in Fractional Sobolev Spaces. Ukr Math J 75, 107–117 (2023). https://doi.org/10.1007/s11253-023-02188-5

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  • DOI: https://doi.org/10.1007/s11253-023-02188-5

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