Continuity with respect to parameter of solutions of nonclassical multipoint boundary value problems in Sobolev spaces

Abstract

For linear systems of ordinary differential equations of order $r\in\mathbb{N}$, we investigate multipoint linear boundary-value problems that depend on a parameter. We find conditions under which the solutions to these problems are continuous with respect to the parameter in the Sobolev spaces $W_p^{n+r}\left([a,b],\mathbb{C}^m\right)$, where $m$, $n+1 \in \mathbb{N}$, and $p\in[1,\infty)$.