On the solvability of inhomogeneous boundary-value problems in Sobolev spaces

TitleOn the solvability of inhomogeneous boundary-value problems in Sobolev spaces
Publication TypeJournal Article
Year of Publication2019
AuthorsAtlasiuk, OM, Mikhailets, VA
Abbreviated Key TitleDopov. Nac. akad. nauk Ukr.
DOI10.15407/dopovidi2019.11.003
Issue11
SectionMathematics
Pagination3-7
Date Published11/2019
Language Ukrainian
Abstract

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.

KeywordsFredholm operator, index of operator, inhomogeneous boundary-value problem, Sobolev space
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