Solvability of linear boundary-value problems for ordinary differential systems in the space  $C^{n}$

Authors

  • V. Soldatov Institute of Mathematics of the National Academy of Sciences of Ukraine, Kyiv; Institute of Applied Mathematics and Mechanics of the National Academy of Sciences of Ukraine, Sloviansk, Donetsk region https://orcid.org/0000-0001-7496-5524

DOI:

https://doi.org/10.3842/umzh.v77i3.8940

Keywords:

Inhomogeneous boundary-value problems, Fredholm operator, Fredholm numbers of an operator, spaces of smooth functions

Abstract

UDC 517.927

We study linear boundary-value problems for systems of first-order ordinary differential equations with the most general boundary conditions in the normed spaces of continuously differentiable functions on a finite closed interval. The boundary conditions are allowed to be overdetermined or underdetermined with respect to the differential system and may contain arbitrary derivatives of the unknown functions. We prove that the problem operator is Fredholm on appropriate pairs of normed spaces, find its  index and $d$-characteristics, and prove the limit theorems for sequences of  characteristic matrices of the investigated boundary-value problems  and $d$-characteristics of the corresponding Fredholm operators.

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Published

07.11.2025

Issue

Vol. 77 No. 3 (2025)

Section

Research articles

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Copyright (c) 2025 V. Soldatov

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How to Cite

Soldatov, V. “Solvability of Linear Boundary-Value Problems for Ordinary Differential Systems in the Space  $C^{n}$”. Ukrains’kyi Matematychnyi Zhurnal, vol. 77, no. 3, Nov. 2025, pp. 206–213, https://doi.org/10.3842/umzh.v77i3.8940.