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 $\varepsilon$ of the solutions to boundary-value problems in the Sobolev spaces $W^n_{\infty}$. We obtain a constructive criterion of the continuous dependence of the solutions of these problems on the parameter $\varepsilon$ for $\varepsilon = 0$. The degree of convergence of these solutions is established.