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

TL;DR

This paper establishes a criterion ensuring the continuity of solutions to a broad class of linear boundary-value problems for higher-order differential systems with respect to parameters, along with convergence estimates.

Contribution

It provides a constructive criterion for solution continuity in parameter-dependent boundary-value problems for general linear differential systems.

Findings

Solutions are continuous with respect to parameters under the new criterion.

A two-sided estimate for the convergence degree of solutions is derived.

The results apply to boundary conditions involving derivatives of various orders.

Abstract

We consider the most general class of linear boundary-value problems for ordinary differential systems, of order $r\geq1$, whose solutions belong to the complex space $C^{(n+r)}$, with $0\leq n\in\mathbb{Z}$. The boundary conditions can contain derivatives of order $l$, with $r\leq l\leq n+r$, 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.