Fredholm One-Dimensional Boundary-Value Problems with Parameters in Sobolev Spaces

For systems of linear differential equations on a compact interval, we analyze the dependence of the solutions of boundary-value problems in the Sobolev spaces W∞n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {W}_{\infty}^n $$\end{document} on a parameter ε. We establish a constructive criterion of continuous dependence of the solutions of these problems on the parameter ε for ε = 0. The rate of convergence of these solutions is determined.