Criterion of continuity with respect to parameter of solutions of multipoint boundary-value problems

Abstract

We investigate a broad class of parameter-dependent multipoint linear boundary-value problems for systems of $r$-order ordinary differential equations whose solutions belong to the complex space $C^{(n)}$, with $1\leq r\leq n\in\mathbb{Z}$. The boundary conditions can contain derivatives $y^{(l)}$, with $1\leq l\leq n$, of the solution $y$ to the system. We obtain a constructive criterion under which the solution is continuous in the normed space $C^{(n)}$ with respect to the parameter.