Parameter-dependent one-dimensional boundary-value problems in Sobolev spaces
arXiv:1704.03774
Abstract
We 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.
13 pages
Cited by in corpus (8)
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- One-dimensional parameter-dependent boundary-value problems in Hölder spaces
- Approximation properties of solutions to multipoint boundary-value problems
- Continuity in a parameter of solutions to boundary-value problems in Sobolev spaces
- On Linear Boundary-Value Problems for Differential Systems in Sobolev spaces