2019/12/12 by Olena Atlasiuk, Atlasiuk, Olena, Vladimir Mikhailets +1
Engineering · Mathematics · #Classical Analysis and ODEs (math.CA) #Differential Equations and Boundary Problems #Differential Equations and Numerical Methods #FOS: Mathematics #Geotechnical and Geomechanical Engineering
paper · pdf · doi:10.48550/arxiv.1912.05993
openalex publication_date 2019/12/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the Fredholm one-dimensional boundary-value problems in Sobolev spaces.We have obtained several important results about the indixes of functional operators, the criterion of their correct well-posedness, the criterion of the continuous dependence of the solutions of these problems on the parameter, the degree of convergence of these solutions, and sufficient constructive conditions under which the solutions of the most general class of multipoint boundary-value problems are continuous with respect to the parameter. Eeach of these boundary-value problems corresponds to a certain rectangular numerical characteristic matrix with kernel and cokernel of 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.