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arXiv · 1604.07029

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

Vladimir A. Mikhailets·Aleksandr A. Murach·Vitalii Soldatov
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Abstract

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 H\"older space $C^{n+1,\alpha}$, with $0\leq n\in\mathbb{Z}$ and $0\leq\alpha\leq1$. 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.

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Vladimir A. Mikhailets, Aleksandr A. Murach, Vitalii Soldatov. 2016-04-24. Continuity in a parameter of solutions to generic boundary-value problems. https://arxiv.org/abs/1604.07029

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