H. Masliuk

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Articles: 1

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

Hanna Masliuk, Vitalii Soldatov

↓ Abstract   |   Article (.pdf)

Methods Funct. Anal. Topology 24 (2018), no. 2, 143-151

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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