Work

Continuity in a parameter of solutions to boundary-value problems in Sobolev spaces

Year: 2025

Type: article

Abstract: We study the most general class of linear inhomogeneous boundary-value problems for systems of ordinary differential equations of an arbitrary order whose solutions and right-hand sides belong to appropriate Sobolev spaces. For parameter-dependent problems from this class, we prove a constructive criterion for their solutions to be continuous in the Sobolev space with respect to the parameter. We also prove a two-sided estimate for the degree of convergence of these solutions to the solution of the nonperturbed problem.

Source: Carpathian Mathematical Publications

DOI: 10.15330/cmp.17.2.433-446

Authors: V.A. Mikhailets, O.M. Atlasiuk

Institutions: National Academy of Sciences of Ukraine, King's College London, Institute of Mathematics, University of Helsinki

Language: English

Topic: Differential Equations and Boundary Problems

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: London Mathematical Society, King's College London, European Commission, Division of Mathematical Sciences

Award: G2314803536