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

• Дата: 2025
• Автори: Soldatov, V., Солдатов, Виталий, Солдатов, Віталій
• Формат: Стаття
• Мова: Українська
• Опубліковано: Institute of Mathematics, NAS of Ukraine 2025
• Онлайн доступ: https://umj.imath.kiev.ua/index.php/umj/article/view/8940
• Назва журналу: Ukrains’kyi Matematychnyi Zhurnal

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.