On the solvability of Fredholm boundary-value problems in fractional Sobolev spaces

  • V. A. Mikhailets Institute of Mathematics of the Czech Academy of Sciences, Institute of Mathematics of the National Academy of Sciences of Ukraine
  • О. М. Atlasiuk Institute of Mathematics of the Czech Academy of Sciences, Institute of Mathematics of the National Academy of Sciences of Ukraine https://orcid.org/0000-0003-0186-3185
  • T. B. Skorobohach NTU of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute” https://orcid.org/0000-0002-0119-8966
Keywords: Fredholm operator, index of operator, inhomogeneous boundary-value problem, fractional Sobolev space

Abstract

UDC 517.927

We study systems of linear ordinary differential equations with the most general inhomogeneous boundary conditions in fractional Sobolev spaces on a nite 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 found. We also present examples showing the constructive character of the obtained results.

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Published
05.02.2023
How to Cite
MikhailetsV. A., AtlasiukО. М., and SkorobohachT. B. “On the Solvability of Fredholm Boundary-Value Problems in Fractional Sobolev Spaces”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 75, no. 1, Feb. 2023, pp. 96 - 104, doi:10.37863/umzh.v75i1.7308.
Section
Research articles