On the solvability of Fredholm boundary-value problems in fractional Sobolev spaces
DOI:
https://doi.org/10.37863/umzh.v75i1.7308Keywords:
Fredholm operator, index of operator, inhomogeneous boundary-value problem, fractional Sobolev spaceAbstract
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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