Vitalii Soldatov- phd
- Researcher at National Academy of Sciences of Ukraine
Vitalii Soldatov
- phd
- Researcher at National Academy of Sciences of Ukraine
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15
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Introduction
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January 2024 - present
Publications
Publications (15)
Solvability of linear boundary-value problems for ordinary differential systems in the space $C^n$. 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 condi...
We consider a broad class of linear boundary-value problems for systems of m ordinary differential equations of order r known as general boundary-value problems. Their solutions y : [a, b] → ℂm belong to the Sobolev space W1rm and the boundary conditions are given in the form By = q, where B: (C(r−1))m → ℂrm is an arbitrary continuous linear operat...
We consider the most general class of linear boundary-value problems for ordinary differential systems, of order $r\geq1$, whose solutions belong to the complex space $C^{(n+r)}$, with $0\leq n\in\mathbb{Z}$. The boundary conditions can contain derivatives of order $l$, with $r\leq l\leq n+r$, of the solutions. We obtain a constructive criterion un...
We introduce the most general class of linear boundary-value problems for systems of first-order ordinary differential equations whose solutions belong to the complex H\"older space $C^{n+1,\alpha}$, with $0\leq n\in\mathbb{Z}$ and $0\leq\alpha\leq1$. The boundary conditions can contain derivatives $y^{(r)}$, with $1\leq r\leq n+1$, of the solution...
In the paper we develop a general theory of solvability of linear inhomogeneous boundary-value problems for systems of first-order ordinary differential equations in spaces of smooth functions on a finite interval. This problems are set with boundary conditions in generic form, that covers overdetermined and underdetermined cases. They also may con...
УДК 517.927 Розглянуто широкий клас лінійних крайових задач для систем звичайних диференціальних рівнянь порядку ~ так звані загальні крайові задачі.Їхні розв'язки належать до простору Соболєва а крайові умови задаються у вигляді де ~ довільний неперервний лінійний оператор.Доведено, що розв'язок такої задачі можна з довільною точністю апроксимуват...
We consider a wide class of linear boundary-value problems for systems of $m$ ordinary differential equations of order $r$, known as general boundary-value problems. Their solutions $y:[a,b]\to \mathbb{C}^{m}$ belong to the Sobolev space $(W_1^{r})^m$, and the boundary conditions are given in the form $By=q$ where $B:(C^{(r-1)})^{m}\to\mathbb{C}^{r...
We consider a wide class of linear boundary-value problems for systems of r-th order ordinary differential equations whose solutions range over the normed complex space (C(n))m of n≥r times continuously differentiable functions y:[a,b]→Cm. The boundary conditions for these problems are of the most general form By=q, where B is an arbitrary continuo...
We consider a wide class of linear boundary-value problems for systems of $r$-th order ordinary differential equations whose solutions range over the normed complex space $(C^{(n)})^m$ of $n\geq r$ times continuously differentiable functions $y:[a,b]\to\mathbb{C}^{m}$. The boundary conditions for these problems are of the most general form $By=q$,...
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...
We introduce the most general class of linear boundary-value problems for systems of first-order ordinary differential equations whose solutions belong to the complex H\"older space $C^{n+1,\alpha}$, with $0\leq n\in\mathbb{Z}$ and $0\leq\alpha\leq1$. The boundary conditions can contain derivatives $y^{(r)}$, with $1\leq r\leq n+1$, of the solution...
We study a broad class of linear boundary-value problems for systems of ordinary differential equations, namely, the problems total with respect to the space C
(n+r)[a, b], where n ∈ ℕ and r is the order of the equations. For their solutions, we prove the theorem of existence, uniqueness, and continuous dependence on the parameter in this space.
