Limit Theorems for the Solutions of Multipoint Boundary-Value Problems with Parameter in Sobolev Spaces

Abstract

We consider the most general class of multipoint boundary-value problems for systems of linear ordinary differential equations of any order whose solutions belong to a given Sobolev space $$ {W}_p^{n+r} $$ , with n ≥ 0, r ≥ 1, and 1 ≤ p ≤ ∞. We establish constructive sufficient conditions under which the solutions of the analyzed problems are continuous with respect to the parameter e for e = 0 in the space $$ {W}_p^{n+r} $$ .