Continuity of the solutions of one-dimensional boundary-value problems in Hölder spaces with respect to the parameter - Maslyuk, H. O. (Ukrains’kyi Matematychnyi Zhurnal, 2017)
We introduce the most general class of linear boundary-value problems for systems of ordinary differential equations of order $r ≥ 2$ whose solutions belong to the complex Hölder space $C^{n+r,α} ([a, b])$, where $n \in Z_{+},\;0 < α ≤ 1$ и $[a, b] \subset R$, and$[a, b] \subset R$. We establish sufficient conditions under which the solutions of these problems continuously depend on theparameter in the H¨older space $C^{n+r,α} ([a, b])$.