On the solvability of inhomogeneous boundary-value problems in Sobolev spaces
DOI:
https://doi.org/10.15407/dopovidi2019.11.003Keywords:
Fredholm operator, index of operator, inhomogeneous boundary-value problem, Sobolev spaceAbstract
We investigate the most general class of Fredholm one-dimensional boundary-value problems in the Sobolev spaces. Boundary conditions of these problems may contain derivatives of higher order than the order of the system of differential equations. 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 boundary-value problem. The conditions for the sequence of characteristic matrices to converge are found.
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Atlasiuk, O. M. & Mikhailets, V. A. (2019). Fredholm one-dimensional boundary-value problems in Sobolev spaces. Ukr. Math. J., 70, No.10, pp. 1526-1537. doi: https://doi.org/10.1007/s11253-019-01588-w
Gnyp, E.V., Kodlyuk, T.I. & Mikhailets, V.A. (2015). Fredholm boundary-value problems with parameter in Sobolev space. Ukr. Math. J., 67, No. 5, pp. 658-667. doi: https://doi.org/10.1007/s11253-015-1105-1
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