Hnyp, YevheniiaMikhailets, VladimirMurach, Aleksandr2022-04-062022-04-062017-03-24Hnyp, Y., Mikhailets, V., & Murach, A. (2017). Parameter-dependent one-dimensional boundary-value problems in Sobolev spaces. <i>Electronic Journal of Differential Equations, 2017</i>(81), pp. 1-13.1072-6691https://hdl.handle.net/10877/15613We consider the most general class of linear boundary-value problems for higher-order ordinary differential systems whose solutions and right-hand sides belong to the corresponding Sobolev spaces. For parameter-dependent problems from this class, we obtain a constructive criterion under which their solutions are continuous in the Sobolev space with respect to the parameter. We also obtain a two-sided estimate for the degree of convergence of these solutions to the solution of the nonperturbed problem. These results are applied to a new broad class of parameter-dependent multipoint boundary-value problems.Text13 pages1 file (.pdf)enAttribution 4.0 InternationalDifferential systemBoundary-value problemSobolev spaceContinuity in parameterArticleThis work is licensed under a Creative Commons Attribution 4.0 International License.