Criterion of continuity with respect to parameter of solutions of boundary-value problems for systems of higher-order differential equations

Abstract

We consider the most extensive class of linear boundary-value problems for systems of ordinary differential equations of order $r\geq1$ whose solutions run through the complex normed space of $n+r$ times continuously differentiable functions on a compact interval, with $0\leq n\in\mathbb{Z}$. The boundary conditions can contain derivatives $z^{(l)}$, with $r\leq l\leq n+r$, of the solution $z$ to the system. For parameter-dependent problems from this class, we obtain a constructive criterion under which their solutions are continuous with respect to the parameter in this normed space.