On solvability of inhomogeneous boundary-value problems in Sobolev - Slobodetskiy spaces
DOI:
https://doi.org/10.15407/dopovidi2020.04.010Keywords:
Fredholm operator, index of operator, inhomogeneous boundary-value problem, Sobolev—Slobodetskiy spaceAbstract
We investigate the most general class of Fredholm one-dimensional boundary-value problems in the Sobolev—Slobodetskiy spaces. Boundary conditions of these problems may contain a derivative of the whole or fractional order. It is established that each of these boundary-value problems corresponds to a certain rectangular numerical characteristic matrix with kernel and cokernel having the same dimension as the kernel and cokernel of the boun dary- value problem. The sufficient conditions for the sequence of the characteristic matrices of a specified bounda ryvalue problems to converge are found.
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