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# One-dimensional parameter-dependent boundary-value problems in Hölder spaces

### 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.

Key words: Differential system, boundary-value problem, continuity in parameter, Hölder space

### Article Information

 Title One-dimensional parameter-dependent boundary-value problems in Hölder spaces Source Methods Funct. Anal. Topology, Vol. 24 (2018), no. 2, 143-151 Milestones Received 23/01/2018; Revised 20/02/2018 Copyright The Author(s) 2018 (CC BY-SA)

### Authors Information

Hanna Masliuk
National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, Peremogy Avenue 37, 03056, Kyiv-56, Ukraine

Vitalii Soldatov
Institute of Mathematics, National Academy of Sciences of Ukraine, Tereshchenkivska Str. 3, 01004 Kyiv-4, Ukraine

### Citation Example

Hanna Masliuk and Vitalii Soldatov, One-dimensional parameter-dependent boundary-value problems in Hölder spaces, Methods Funct. Anal. Topology 24 (2018), no. 2, 143-151.

### BibTex

@article {MFAT1054,
AUTHOR = {Masliuk, Hanna and Soldatov, Vitalii},
TITLE = {One-dimensional parameter-dependent boundary-value
problems in Hölder spaces},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {24},
YEAR = {2018},
NUMBER = {2},
PAGES = {143-151},
ISSN = {1029-3531},
URL = {http://mfat.imath.kiev.ua/article/?id=1054},
}

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