Continuity in a parameter of solutions to generic boundary-value problems

Abstract

We introduce the most general class of linear boundary-value problems for systems of first-order ordinary differential equations whose solutions belong to the complex Hölder space $C^{n+1,\alpha }$, with $0\le n\in \mathbb{Z}$ and $0\le \alpha \le 1$. The boundary conditions can contain derivatives $y^{(r)}$, with $1\le r\le n+1$, of the solution $y$ to the system. For parameter-dependent problems from this class, we obtain constructive criterion under which their solutions are continuous in the normed space $C^{n+1,\alpha }$ with respect to the parameter.

15 pages