On the Continuity in a Parameter for the Solutions of Boundary-Value Problems Total with Respect to the Spaces $C^{(n+r)}[a, b]$

Abstract

We study a broad class of linear boundary-value problems for systems of ordinary differential equations, namely, the problems total with respect to the space $C^{(n+r)}[a, b]$, where $n ∈ ℕ$ and $r$ is the order of the equations. For their solutions, we prove the theorem of existence, uniqueness, and continuous dependence on the parameter in this space.