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arXiv · 1610.07996

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

Vladimir Mikhailets·Aleksandr Murach·Vitalii Soldatov
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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.

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Vladimir Mikhailets, Aleksandr Murach, Vitalii Soldatov. 2016-10-25. A criterion for continuity in a parameter of solutions to generic boundary-value problems for higher-order differential systems. https://arxiv.org/abs/1610.07996

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