Fredholm one-dimensional boundary-value problems with parameter in Sobolev spaces

Abstract

For systems of linear differential equations on a compact interval, we investigate the~dependence on a parameter $\epsilon$ of the solutions to boundary-value problems in the Sobolev spaces $W_{\infty }^n$. We obtain a constructive criterion of the continuous dependence of the solutions of these problems on the~parameter $\epsilon$ for $\epsilon =0$. The degree of convergence of these solutions is established.

References in corpus (1)

• Parameter-dependent one-dimensional boundary-value problems in Sobolev spaces

Cited by in corpus (4)

• On the solvability of Fredholm boundary-value problems in fractional Sobolev spaces
• On Linear Boundary-Value Problems for Differential Systems in Sobolev spaces
• Solvability of linear boundary-value problems for ordinary differential systems in the space $C^n$
• Continuity in a parameter of solutions to boundary-value problems in Sobolev spaces