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arXiv · 1802.02019

One-dimensional parameter-dependent boundary-value problems in H\"older spaces

Hanna Masliuk·Vitalii Soldatov
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Abstract

We study the most general class of linear boundary-value problems for systems of $r$-th order ordinary differential equations whose solutions range over the complex H\"older space $C^{n+r,\alpha}$, with $0\leq n\in\mathbb{Z}$ and $0<\alpha\leq1$. We prove a constructive criterion under which the solution to an arbitrary parameter-dependent problem from this class is continuous in $C^{n+r,\alpha}$ with respect to the parameter. We also prove a two-sided estimate for the degree of convergence of this solution to the solution of the corresponding nonperturbed problem.

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BibTeXRIS

Hanna Masliuk, Vitalii Soldatov. 2018-02-06. One-dimensional parameter-dependent boundary-value problems in H\"older spaces. https://arxiv.org/abs/1802.02019

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