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arXiv · 2005.03494

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

Olena Atlasiuk·Vladimir Mikhailets
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Abstract

We consider 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.

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Olena Atlasiuk, Vladimir Mikhailets. 2025-12-18. Continuity in a parameter of solutions to boundary-value problems in Sobolev spaces. https://arxiv.org/abs/2005.03494

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