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<p>We study linear boundary-value problems for systems of the 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 may be overdetermined or underdetermined with respect to the differential system and may contain arbitrary derivatives of the unknown functions. We show that the operator of the problem is Fredholm on the proper pairs of normed spaces, find its index and <i>d</i>-characteristics, and prove limit theorems for the sequences of characteristic matrices of the investigated boundary-value problems and the <i>d</i>-characteristics of the corresponding Fredholm operators.</p>

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Solvability of Linear Boundary-Value Problems for Ordinary Differential Systems in the Space CN

  • 期刊论文

  • 发表日期：

    2025年8月1日

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  • Vitalii Soldatov

摘要

We study linear boundary-value problems for systems of the 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 may be overdetermined or underdetermined with respect to the differential system and may contain arbitrary derivatives of the unknown functions. We show that the operator of the problem is Fredholm on the proper pairs of normed spaces, find its index and d-characteristics, and prove limit theorems for the sequences of characteristic matrices of the investigated boundary-value problems and the d-characteristics of the corresponding Fredholm operators.