Continuity in a parameter of solutions to generic boundary-value problems

• Main Authors: Vladimir Mikhailets, Aleksandr Murach, Vitalii Soldatov
• Format: Article
• Language: English
• Published: University of Szeged 2016-09-01
• Series: Electronic Journal of Qualitative Theory of Differential Equations
• Subjects: differential system; boundary-value problem; hölder space; continuity in parameter
• Online Access: http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1&paramtipus_ertek=publication&param_ertek=4905

We introduce the most general class of linear boundary-value problems for systems of first-order ordinary differential equations whose solutions belong to the complex Hölder space $C^{n+1,\alpha}$, with $0\leq n\in\mathbb{Z}$ and $0\leq\alpha\leq 1$. The boundary conditions can contain derivatives $y^{(r)}$, with $1\leq r\leq n+1$, of the solution $y$ to the system. For parameter-dependent problems from this class, we obtain constructive criterion under which their solutions are continuous in the normed space $C^{n+1,\alpha}$ with respect to the parameter.