A criterion for continuity in a parameter of solutions to generic boundary-value problems for higher-order differential systems

We consider the most general class of linear boundary-value problems for ordinary differential systems, of order $r\ge 1$, whose solutions belong to the complex space $C^{(n+r)}$, with $0\le n\in \mathbb{Z}$. The boundary conditions can contain derivatives of order $l$, with $r\le l\le n+r$, of the solutions. We obtain a constructive criterion under which the solutions to these problems are continuous with respect to the parameter in the normed space $C^{(n+r)}$. We also obtain a two-sided estimate for the degree of convergence of these solutions.